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Increasing computational power has led to the expansion of civil engineering research into using machine learning concepts for developing improved design strategies. These strategies are particularly useful for the design of extra-terrestrial habitats under uncertain environmental conditions. This paper focuses on building an unsupervised machine learning model (convolutional autoencoder) capable of detecting patterns in arch shapes and differentiating between their stress and displacement contours. Foremost, detailed discussions of the model's architecture and input data are presented. The variation of arch shapes and contours between cluster centroids in the latent space is determined, proving the capability of optimisation by moving towards clusters with optimal contours. Finally, a regression model is built to investigate the relationship between the input geometric variables and the latent space representation. We prove that the autoencoder and regression models produce arch shapes with logical structural contours given a set of input geometric variables. The results presented in this paper provide essential tools for the development of an automated design strategy capable of finding optimal arch shapes for extra-terrestrial habitats. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of non-homogeneous elastic foundations on the free vibration characteristics of functionally graded graphene platelets reinforced composite plates submerged in fluid medium. A novel aspect of this study lies in exploring various distributions of the foundation, positioned either centrally within the plates or along their edges. The stiffness of the foundation is computed using Selvadurai's method, which accounts for subgrade soil properties and foundation depth. Material properties of the plates are examined by employing the rule of mixtures alongside the Halpin–Tsai micromechanical model. Hydrostatic pressure and free surface waves are not considered, given the assumption of an ideal and incompressible fluid. The theoretical framework is grounded in a novel inverse trigonometric shear deformation plate theory, where the transverse shear stress distribution is established using a newly developed inverse trigonometric function. The equations of motion are efficiently resolved through Galerkin's method. The efficacy of this approach lies in its utilization of integration to address the distribution issue of the foundation, obviating the need for deploying intricate algorithms. The proposed theory demonstrates enhanced accuracy in predicting natural frequencies compared to other published shear deformation plate theories. Moreover, this paper delves into the effect of material properties and the fluid environment on the natural frequencies of the structures. Particularly significant is our thorough investigation of the impact of variations in the locations, material properties, and sizes of the foundation on the free vibration of these plates, all of which bear great importance in structural design. [ABSTRACT FROM AUTHOR]

This paper introduces a structural design which has superior energy harvesting ability. The proposed structure is based on the ability of most periodic structures to prohibit elastic waves from propagating in a specific frequency range of the phonon band gap. By leading into acoustic black hole (ABH) units and utilizing the energy concentration characteristics of the ABH structure, the filtering effect can be made more significant. These two characteristics can produce significant strain and energy localization, which is conducive to energy harvesting. In this paper, we obtained ABH unit capable of producing broadband gaps by adjusting the geometric parameters of the ABH structure, and chose a cantilever as the research object for energy harvesting, by applying a piezoelectric patch on the unit located near the fixed end to gain a broader application in the actual situation. The results show that the beam combining the energy concentration characteristics of band gap and ABH structure has a significant improvement in energy harvesting efficiency. Optimization on the parameters of ABH unit shows that the band gap characteristic of the periodic ABH structure can further optimize the energy harvesting efficiency of practical energy harvesters, and opens up a new possibility of energy harvesting of ABH structure. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the behaviour of two symmetric mode-III collinear cracks in a functionally graded material (FGM). The fundamental goal of this paper is to provide insight on the interaction of two cracks in FGMs with the strain gradient effect. To assess the influence of gradient elasticity, we have considered two key parameters ℓ and ℓ ′ , which describe the size scale effect caused by the underlying microstructure and are related to volumetric and surface strain energy, respectively. The crack boundary value problem have been solved by the approach involving Fourier transforms and the innovative hyper-singular integro-differential equation method, where the integral equation contains the two terms in integrals for the both cracks. A system of equations has been constructed by employing the Chebyshev polynomial expansion and then by choosing the suitable collocation points the system of equation have been solved. Our investigation involves the determination of stress intensity factors at both crack tips. These factors are vital for understanding the material's fracture behavior and structural integrity. Furthermore, we explore the variations in the displacement profile when the distance between the cracks is reduced to close proximity. This particular scenario is of significant interest as it provides insights into how the interaction between the cracks impacts the overall structural response. [ABSTRACT FROM AUTHOR]

Nowadays, the dynamic behavior of rolling stocks is an essential problem. In dynamic simulation, the correct wheel-rail contact modeling is an important task. In this paper, the stiffness of the wheel-rail contact zone is found by a new, direct, and simplified formulation. This subject is developed by applying more details, such as surface roughness based on the surface topography and hardening effects of a real contact problem. These characteristics have not been considered altogether in other similar works. In this work, the contact stiffness and frequency results are obtained for different material properties and verified with analytical and experimental research. It is shown that the presented new direct method with an acceptable accuracy is easier to use than the complicated existing methods. This paper discusses the effects of contact parameter variations on contact stiffness and frequency. For example, it is shown that the contact stiffness decreases by increasing the surface roughness and increases by increasing the strain-hardening factor. [ABSTRACT FROM AUTHOR]

A matter of fact is that extremal principles have been introduced in mechanics in more (Euler, Lagrange) or less (Hamilton) than 200 years ago. One may also observe an impact of thermodynamic extremal principles based on maximum dissipation due to all the entropy production expressed in several disciplines. According fields are theory of communication, statistical mechanics and later physics of earth since already 70 years. The current paper offers some (historical) overview on several applications. "Ziegler's principle" is an implementation of the maximum entropy production going out to the dissipation and yielding a maximum dissipation. The goal of this paper is now the implementation of this extremal principle performed along an algebraic concept. Such a concept can be extended to a system with several internal variables as outlined by Coleman and Gurtin in context with the Gibbs (free) energy. [ABSTRACT FROM AUTHOR]

In this paper, the flexural wave propagation and its control of a novel piezoelectric composite pipe conveying fluid are investigated. Dual piezoelectric layers used as sensor and actuator are periodically arranged on the pipe, and a feedback amplifying circuit is applied from sensor to actuator, forming a self-powered phononic crystal (PC) control structure. The vibration reduction performance can be actively tuned by adjusting the feedback control gain instead of conventional changing the construction of pipe itself. The pipe is composed of functionally graded material (FGM), in which the material properties vary continuously along the radial direction, and a poroelastic medium is introduced. By using the Timoshenko beam theory and Hamilton's principle, a set of electromechanical coupling equations governing flexural vibration of the pipe is deduced. The band structure, band gap (BG) distribution and frequency response are presented by applying the spectral element technology. Comprehensive parametric studies are carried out. The results obtained validate the excellent vibration control effect of the proposed design, and further demonstrate the significant impacts of material, piezoelectric layers, feedback control and flowing fluid on the BG characteristics. This paper is expected to provide a technological reference for the vibration and elastic wave control of engineering composite pipe structures. [ABSTRACT FROM AUTHOR]

Compared to acoustic cloak, elastic wave cloak is difficult to construct due to inapplicability of form invariance for the control equations. Traditional elastic wave cloak is limited to Willis material or Cosserat material. In this paper, a modified symmetric design method for elastic wave cloak is proposed for underground protective structures based on a multi-center coordinate transformation scheme. First, a symmetry function is established to depict the degenerated symmetric elastic tensor by geometric averaging the elastic tensor components. The shielding performance of the symmetric method proposed in this paper is compared with that of the symmetric method in the literature. The finite element simulation results show that the symmetric cloak proposed in this paper can better reduce the displacement and shield the elastic wave. The proposed method is then used to construct elastic wave cloak for the arch shaped structure which is common in underground protective structures. A multi-center coordinate transformation scheme is applied for this purpose by dividing the arch structure into multiple coordinate transformation regions each with a local coordinate system. The shielding performance of the underground protective cloak against elastic waves with different wave incident directions and frequencies is discussed in details. The simulation results indicates that the symmetrical underground protective cloak can effectively detour the incident elastic waves, and has a good shielding effect at frequencies ranging from 50 to 1000 Hz. [ABSTRACT FROM AUTHOR]

This paper addresses the exact controllability of vibrations in a three-dimensional Cosserat elastic solid body using mathematical techniques such as operator theory and semigroup methods. The verification of exact (shape) controllability is accomplished through the application of the Hilbert Uniqueness Method, which involves investigating the boundary observability for the dual system. In partial differential equations control theory, the concept of exact observability for the dual system is fundamental to achieving exact controllability, although it differs from the common understanding of controllability. While control theory for systems governed by ordinary differential equations (ODEs) has a relatively formal and standardized approach, systems with distributed parameters, such as the Cosserat medium under consideration, involve a multitude of technical inequalities that must be established. Notably, Cosserat media possess six degrees of freedom for microstructures, in contrast to classical media with only three degrees of freedom. Consequently, exact control is required for all six variables, encompassing three translational and three rotational degrees of freedom, while classical media only necessitate the exact control of three translational variables. The paper concludes with a series of numerical studies utilizing the fast Fourier transform (FFT) and various simulations, which serve to validate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

The fundamental equations and some special solutions of contact mechanics for solid fractal surfaces are proposed in this paper. Firstly, as for fractal solid surface, the probability distribution equation of height without pressure, the probability distribution equation of vertical displacement with pressure and the probability distribution equation of contact stress are established. Secondly, considering the adhesion force, a special solution is given for the probability distribution equation of contact stress when the fractal index is 2. Finally, when the area ratio of multi-scale contact is 0.5, the influence of different derivative orders on the results is discussed. In this paper, a complete analytical framework is given for the static multi-scale contact mechanics. [ABSTRACT FROM AUTHOR]

This paper presents a forced vibration analysis of open doubly curved sandwich panels subjected to a moving constant force. In this paper, the effect of softness of the core is considered by implementing a semi-layerwise theory. To this aim, the first-order shear deformation theory is adopted for the face sheets and a higher-order theory which was obtained based on 3D elasticity theory is considered for the core. The presented formulation is general and as the deepness parameter is accounted in the strain–displacement relations, the formulation can be used for a wide range of deep as well as shallow doubly curved shells. To obtain the dynamic response of the system, the finite element method (FEM) along with the Newmark method is used. The proposed element is a higher-order one with nine nodes and each node has fifteen degrees of freedom. The effect of various parameters such as length-to-thickness ratio, in-plane aspect ratio, boundary conditions, lamination scheme, and fiber orientation angles on the dynamic response of the structure is examined. Additionally, the critical velocity of the force at which the structure experiences maximum dynamic deflection is obtained in each case. The results show that as the length-to-thickness ratio of the structure increases, the dynamic magnification factor curve increases with respect to non-dimensional velocity. This study provides insights into the dynamic behavior of doubly curved sandwich panels with soft cores and can aid in the design of such structures for specific applications. The results of this study can also serve as a benchmark for future studies on the forced vibration behavior of doubly curved sandwich panels. [ABSTRACT FROM AUTHOR]

Dynamic reliability evaluation of large-scale reinforced concrete (RC) structures is one of the most challenging problems in engineering practices. Although extensive endeavors have been devoted to mechanical analysis of concrete structures in the past decades, it was recognized that the randomness from both structural parameters and excitations have significant effects on the dynamic behaviors of structures with complex nonlinearity, damage, energy dissipation, and plasticity. Thus, great difficulty exists in evaluating the nonlinear stochastic responses and dynamic reliability of the real-world complex structures of large degrees of freedom. In the present paper, a physically driven method for refined probabilistic response and seismic reliability evaluation of real-world RC structures is proposed via synthesis of the refined mechanical analysis and the physically-based uncertainty propagation. In this method, the material parameters can be treated as probabilistically dependent random variables characterized by vine copulas, and the ground motion is modeled by non-stationary Clough–Penzien spectrum. The uncertainty propagation of arbitrary response quantity(-ies) of interest is governed by the dimension-reduced probability density evolution equation (DR-PDEE). The intrinsic drift coefficients in the DR-PDEE are the physically driven force for the uncertainty propagation and can be identified via data from representative dynamic analyses of the structure. The time-variant reliability of the structures can be captured by solving the physically driven DR-PDEE, which cannot be achieved by the general Monte Carlo simulation (MCS) due to the prohabitively large computational cost. Finally, a practical engineering application is shown in this paper for the probabilistic response and seismic reliability evaluation of a 24-story RC shear wall structure with nearly 280,000 degrees of freedom (DOFs). [ABSTRACT FROM AUTHOR]

In this paper, a dynamic interaction model of the coupled system of railway bridge, foundation, subsoil, ballast, track, and high-speed train is presented, with special emphasis on the longitudinal interaction between the track and the bridge structure, taking into account the flexibility of the ballast. After a description of the model of this interaction system, the equations of motion are given separately for each subsystem. The discretization of the bedded rails is performed by two different approaches. In the first approach, the deflection of the rails is expanded into the eigenfunctions of a finitely long bedded beam representing the rails. In the second, simplified approach, the track response is represented by a superposition of the static deflection of the infinitely long bedded beam due to a concentrated load. The coupling of the bridge structure with the track is achieved by a component mode synthesis technique, which in the first approach leads to a representation of the equations of motion in state-space. A discrete substructure technique is used to couple this subsystem with the train model. The two presented strategies are verified by comparison with results of a finite element model of this interaction system. Several application examples reveal the influence of the horizontal track–bridge interaction and other modeling parameters on the dynamic bridge response. [ABSTRACT FROM AUTHOR]

In structural dynamics, response modeling relies on parameters, which are to be identified by experiments. However, for satisfactory results, the design of such experiments is laborious and requires a comprehensive physical insight, which is limited. Furthermore, accurate models are high dimensional and can operate only with a large set of parameters, which increases the experimental effort even more. Efficient data sampling methods have been addressed in studies within areas of design of experiments and active learning. However, generating a data set for nonlinear dynamic systems poses an increased degree of difficulty, since the system needs to be guided through unknown dynamics to collect the desired data points. In this paper, we address this challenge by introducing a theoretical data generation framework for testing-integrated modeling. In the proposed framework, we use feedforward neural networks (FNNs) for inverse modeling of the nonlinear restoring force of the systems. By sequentially evaluating the accuracy of the trained model on a given test data set, the excitation signal applied on the system is adapted to generate optimal response data which allow the FNN model to learn the restoring force behavior. Hence, data generation is posed as an optimization problem and pattern search algorithm is used for sampling. The performance of the proposed framework is evaluated, and it is shown that it outperforms unsupervised sampling methods. [ABSTRACT FROM AUTHOR]

The indirect approaches based on the responses of specially designed moving vehicles on bridges to extract bridge dynamic properties have received great research attention. Wavelet transform (WT) is shown to be a useful tool for the analysis of vehicle responses and bridge damage detection in the vehicle-bridge interaction system. However, past studies have demonstrated that road surface roughness poses difficulty in applying wavelet analysis to successfully detect bridge damage. In this paper, a two-step method is proposed for bridge damage detection based on WT analysis of the residual contact response of the front and rear vehicle wheels of a four degrees of freedom (4-DOF) moving vehicle to reduce the influence of road surface roughness. In the first step, the generalized Kalman filter under unknown input (GKF-UI) developed by the authors is used to identify the unknown contact forces and the state vector of the vehicle. Due to the advantages of GKF-UI, acceleration and displacement sensors can be installed conveniently on the vehicle body instead of on the wheel axles in previous studies. Then, the contact-point bridge deflection responses of the front and rear vehicle wheels are estimated from the identified contact force and vehicle state. In the second step, the residual contact-point bridge deflection response is obtained by subtracting the front contact-point bridge deflection and rear contact-point bridge deflection with a time shift to reduce the influence of road surface roughness. Then, the locations of bridge damage can be identified based on WT of the singularities of residual contact-point bridge deflection response. Numerical examples of bridge damage detection demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The identification of frequency zones where waves propagate freely (i.e., propagation zones) and where they are attenuated (i.e., attenuation zones) in a railway track, plays an important role in a number of applications, such as nondestructive testing, structure-borne noise prediction, and vibration control. This paper presents a numerical model based on the wave finite element method to study wave propagation and attenuation in periodic supported rails. The model involves postprocessing of element matrices of a rail span (i.e., rail segment between two supports), which is modeled using three-dimensional finite elements meshed through the cross section. The model uses solid elements to capture the complex cross-sectional deformation of the waves and considers the dimensions of the periodic supports. In order to obtain accurate results, the stiffness and the damping coefficients of the supports are calibrated through a finite element model updating procedure that utilizes the modal parameters and the attenuation coefficients obtained from experiments. The results demonstrate that the proposed model is capable of (i) capturing the classic vibrational modes (i.e., vertical and lateral bending), (ii) describing the complex cross-sectional deformation and the mode conversions, and (iii) obtaining the wave propagation and attenuation regions of periodic supported rails. [ABSTRACT FROM AUTHOR]

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort. [ABSTRACT FROM AUTHOR]

The paper presents a semi-analytical method, named the Double Legendre Polynomial Method (DLPM), which is extended for modeling the axisymmetric free vibration of a functionally graded piezoelectric (FGP) hollow cylinder resonator. The FGP resonator is composed of two-phase graded piezoelectric materials, Lead zirconate titanate (PZT4) and aluminum nitrid (AlN), on the top and bottom surfaces, respectively, where the material properties gradually change along the thickness direction. The integration of FGP materials with piezoelectric materials is an innovative aspect in material science, and this paper explores their dynamic behavior, providing insights into their mechanical and electrical properties and contributes to expand our understanding of the axisymmetric free vibration of FGP hollow cylinder resonators as a crucial factor for optimizing their performance across a wide range of applications, including sensors, actuators, energy harvesting, and structural health monitoring systems. The DLPM is applied to solve the wave governing differential equations of motion, offering a new tool for studying the dynamic behavior of FGP hollow cylinders under axisymmetric vibration. The study investigates the effects of the diameter-thickness ratio on the effective electromechanical coupling coefficient and the resonant and anti-resonant frequencies of the FGP hollow cylinder. The results show that as the diameter-thickness ratio increases, the frequency-diameter product appears to become more stable. This observation is a valuable insight for optimizing the design of these resonators. Furthermore, the study presents the electrical input admittance, the natural frequencies as well as the mechanical displacement and electric potential profiles of the resonator. All the provided results are based on the calculation of the resonant frequencies. The validity of the presented results was verified by the comparison with the existing ones reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, an exact elasticity solution of functionally graded material (FGM) rectangular plate under cylindrical bending is presented. The formulation is based on the displacement approach in which 3D elasticity equations are reduced to 2-D equations using plane-strain conditions. In the present formulation, an exact elasticity solution is feasible due to the consideration of simply supported boundary conditions with applied loads expressed in harmonic forms. Functionally graded material (FGM) infinite rectangular plate subjected to realistic transverse normal loads are analyzed. Solutions have been presented for FGM plate with various aspect ratios and gradation factors. Variation of displacements and stresses through the thickness has been investigated for the FGM plate subjected to single sinusoidal load, uniformly distributed load, hydrostatic load, and strip load. Validation of results is presented using reference results in the literature. The extensive results presented in this paper can be served as benchmark solutions for the assessment of improved plate theories. [ABSTRACT FROM AUTHOR]

Interference fit is a classic issue in mechanical engineering. In this paper, under the axial/spherical symmetrical assumption, the analytical solutions for the interference fit problem of the internal and external functionally graded materials (FGMs) hollow cylinder/spherical shell are obtained. Herein, the unified form of the FGMs hollow cylinder/spherical shell basic equation is given by introducing a geometric parameter. The degradations of the analytical solutions in this paper are consistent with the corresponding results in the existing work. The effects of interference value, structural material parameters, and geometric dimensions on the displacement and stress distribution of FGMs structures are analyzed numerically. [ABSTRACT FROM AUTHOR]

In this paper, an equivalent imperfect interface model of PN homojunction/ heterojunction of piezoelectric semiconductor for the multi-field coupled wave propagation is proposed firstly. PN junction is a special structure formed by the contact of two different types of doped semiconductors, which has been used extensively in semiconductor devices. Due to the gradient distribution of the electric potential and carrier concentration in PN junction of finite thickness, the reflection and the transmission will arise when the coupled waves propagate through PN junction. The effects of the PN junction on the wave propagation will be much more complicated by the accurate estimation. An equivalent imperfect interface model without thickness but with seven interface parameters is established to simulate the effects of PN junction which largely reduces the calculation cost. The numerical examples are provided and compared with the state transfer matrix method and the piecewise homogenization method. Energy flux of the reflected and transmitted waves are estimated, and the energy conservation is checked to verify reliability of the numerical results. [ABSTRACT FROM AUTHOR]

The extended multiscale finite element method (EMsFEM) shows great efficiency and accuracy for analyzing the mechanical behavior of heterogeneous materials, especially for non-periodic multiscale materials. The conventional EMsFEM requires solving boundary value problems repeatedly on each coarse-scale element to construct the numerical base functions related to the material parameters of fine-scale element, which constitutes the main part of computational resources. This paper presents a physics-informed neural network (PINN) enhanced EMsFEM to further improve the efficiency of multiscale mechanical analysis. Since the boundary value problems are based on the same solution domain and boundary conditions, a PINN is elaborately designed to solve them described by mechanical equations. The input parameters of PINN contain the material parameters of the fine-scale elements inside the coarse-scale element; therefore, the PINN can quickly map the heterogeneous material properties to the displacements inside the coarse-scale element and greatly improve the construction efficiency of the numerical base functions. To enhance the computational accuracy, the domain decomposition technique is applied to characterize the heterogeneity of the elements, and an unbiased construction method is developed to obtain the numerical base functions that simultaneously ensure the computational consistency and normalization condition. In addition, to further improve the computational efficiency, the construction process of numerical base functions is simplified according to the approximately ergodic property of the network for randomly physical fields. Several representative numerical examples are presented to demonstrate the high efficiency and accuracy of the proposed PINN-enhanced EMsFEM. The method is of high universality since the PINN does not need to be retrained as the geometry of the entire domain and loading of the problem change, the network structure is only related to the length ratio of the coarse- and fine-scale elements. [ABSTRACT FROM AUTHOR]

In this paper, a new type of auxetic honeycomb is designed, which introduces arc walls into the concave hexagonal honeycomb cells and has higher specific energy absorption. The deformation modes and energy absorption of the designed honeycomb are analyzed by using three methods including finite element, compression experiment and machine learning methods. A fully connected two-hidden layer backpropagation deep neural network (BP-DNN) is developed to predict the energy absorptions of the honeycomb with different geometric parameters. It is found that the error of the validation set is low, and the average correlation coefficient of the validation set is 99.2%, which indicates that the neural network can obtain good predictions. The sensitivity analysis of the input parameters shows that the thickness t has the highest sensitivity, and the ratio of the length of the straight wall to the height has the lowest sensitivity to the energy. In addition, the neural network developed can also predict the mechanical properties of the honeycombs outside the parameter range of the training set and the results are consistent with that of the sensitivity analysis. The DNN provides a fast and accurate method for the energy absorption of honeycombs, which is expected to speed up the optimization and design process of honeycomb structures. [ABSTRACT FROM AUTHOR]

In this paper, the phenomenon of bursting oscillations and control of the magnetically coupled bistable broadband piezoelectric energy harvesting (PEH) system under low-frequency acceleration excitation are studied. Combined with the external excitation term, potential energy function and various electromechanical factors, their effects on the bursting oscillations and energy harvesting efficiency are theoretically analyzed, aiming to provide a reference for the reliability design of the bistable piezoelectric energy harvesting system. In addition, the system is controlled by time-delay feedback to achieve the purpose of vibration reduction and energy collection. First of all, according to the fast and slow dynamic analysis method, the external excitation term is regarded as the slow variable, which is used as the control parameter to adjust the dynamic behavior of the fast subsystem. The motion law and bifurcation mechanism of the system are analyzed through the time history diagram, phase diagram and transition phase diagram when the system presents bursting oscillations. Second, the effects of parameters such as external excitation amplitude and external excitation frequency on the energy harvesting efficiency were analyzed. Then, focusing on the bursting oscillations of the system, the cooperative control is used to suppress the bursting oscillation phenomenon, so that the system can be operated stably. Finally, time-delay feedback control is applied to the PEH system to achieve the purpose of vibration reduction and energy collection. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical formulation of a transient problem for an anisotropic plate on an elastic-inertial foundation. The plate features local fixations of various types, located along its perimeter. The plate's contour can be arbitrary. It is subjected to a load with a time-varying amplitude. An original method for solving the posed problem has been developed and implemented. By applying integral transformations, a fundamental solution for an unlimited anisotropic plate has been constructed. This solution is used to formulate resolving integral representations for investigating the transient dynamics of the plate with local supports. Integral representations for transient displacements, moments, and rotation angles of the plate sections have been obtained using the method of compensating loads. The time-dependent compensating loads are determined from the solution of a system of Volterra integral equations of the first kind. By employing the quadrature method at each time step, the problem of compensating loads is reduced to solving a system of linear algebraic equations. A comparison of the obtained results with solutions derived using the finite element method is conducted. Graphical results of the calculations and an evaluation of the convergence of the proposed method are provided. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in high-performance micro/nano-electro-mechanical systems. In this paper, the damping characteristics in semiconductor microbeam are studied under coupled carrier-thermo-elastic theory. Using conventional LR model and considering the effect of carrier, the governing equations for TED in semiconductor beam were obtained and the analytical solution for temperature and carrier density was obtained using complex frequency method. The expression for inverse quality factor was given by solving the vibration equation. The effects of cantilever beam size, material parameters, temperature, and doping concentration on TED were studied, and the results showed that the carrier has significant influence on the dissipation performance of semiconductor microstructures. The study also indicated that when carrier characteristics are ignored, this conclusion can degenerate into classical TED results under LR model. [ABSTRACT FROM AUTHOR]

In this paper, an effective numerical Bernstein polynomials operational matrix is exploited to study the nonlinear forced vibration of fractional viscoelastic curved beam with viscoelastic nonlinear boundary conditions, for the first time. The Caputo fractional derivative is employed to incorporate viscoelastic material having nonlinear behavior. Based on Euler–Bernoulli beam theory and von Kármán geometric nonlinearity, the governing equation of viscoelastic curved beam which is a nonlinear integro-partial fractional differential equation is introduced. Based on the collocation method of Bernstein polynomials approximation, the generalized integer-order operational matrices of differentiation and integration as well as fractional-order operational matrix of differentiation are derived. Using Bernstein polynomials operational matrices (BPOM), the nonlinear static problem is discretized; then, it is solved via Newton's method. To compute the linear vibration mode, the linear vibration problem is discretized via BPOM and it is solved as a linear eigenvalue problem. Discretized by the Galerkin approximation, the fractional-order nonlinear integro-partial differential equation is transformed into a nonlinear fractional-order duffing-type equation. The fractional-order duffing equation is discretized using BPOM resulting nonlinear eigenvalue problem, which can be easily solved by pseudo-arc length continuation algorithm. The effects of the Caputo fractional derivative order, foundation parameters, amplitude of initial curvature, viscoelastic parameters and amplitude of excitation force on the nonlinear forced vibration of the viscoelastic beam are investigated through a detailed parametric study. The proposed procedure is supportive in the analysis and design of curved viscoelastic structure with non-classical viscoelastic boundary conditions under the dynamic mechanical loads. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear forced vibration responses of axially moving functionally graded carbon nanotube reinforced composite (FG-CNTRC) rectangular thin plates are investigated. In the frame of classical plate theory and von Kármán geometric nonlinear theory, the nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are established by Hamilton's principle and discretized through the Galerkin method. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in the literature. The frequency response curves (FRCs) of axially moving FG-CNTRC plates subjected to transverse harmonic concentrate excitation are calculated by using the incremental harmonic balance (IHB) method. The stability and bifurcation characteristics of period solutions obtained through the IHB method are analyzed by Floquet theory. The isolated detached resonance curves (DRCs) are observed inside the main continuous FRCs of axially moving FG-CNTRC plates. Saddle-node bifurcation, Hopf bifurcation, quasi-periodic motion and the internal resonance caused by the modal coupling effect are analyzed. The numerical results illustrate the effects of the CNT distribution, volume fraction, axially moving velocity, aspect ratio and width-to-thickness ratio on the nonlinear dynamic responses of axially moving FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

The paper is concerned with the study of a chemical reaction between diffusing and solid constituents. The reaction is localized at a propagating reaction front and is accompanied by a transformation strain, which generates stresses affecting the reaction rate. The effect of mechanical stresses on the velocity of the reaction front is taken into account basing on the concept of a chemical affinity tensor. The initial boundary value problem of the propagation of the chemical reaction front is discussed by the example of an axisymmetric problem for a reaction in a cylinder in the case of linear elastic solid constituents. The stage of initial accumulation of the diffusing constituent and the stage of the propagation of the reaction front after its separation from the outer boundary of a body are distinguished. The time preceding the start of the reaction is determined. Conditions at the propagating chemical reaction front for the diffusion problem are discussed. A comparative analysis of the solutions obtained in the quasi-stationary and nonstationary formulations of the diffusion problem is carried out, taking into account and without taking into account the influence of the initially accumulated diffusing constituent on the reaction front velocity, as well as for the case of the absence of diffusion in the untransformed material. [ABSTRACT FROM AUTHOR]

An investigation of the basic nanoconvective flow to be applied in evaluating the limit of validity of the transient hot wire experimental (THW) method for nanofluids is presented. Analytical solutions for the basic temperature, basic nanoparticles volume fraction, and basic natural convection velocity are being derived and analyzed. These basic solutions are needed in follow-up linear and nonlinear stability analyses aiming to establish the time required for natural convective heat flux to develop and invalidate transient hot wire experimental results. While the first part of the paper presents the current status of knowledge related to the transient hot wire experimental method and the theoretical aspects governing the validity of the method, the second part aims at presenting new results that can provide additional and more accurate conditions for the validity of that experimental method. [ABSTRACT FROM AUTHOR]

The dispersion and reflection characteristics of coupled waves in the piezomagnetic solid with flexomagnetic microstructure effect are studied in this paper. The flexomagnetic effect, strain gradient effect and micro-inertia effect are introduced into the constitutive equation and the governing equation to establish the wave propagation theory in the piezomagnetic solid with flexomagnetic microstructure effect. The secular equation of wave propagation is derived, and the properties of five coupled waves are analyzed. The dispersion characteristics of coupled waves and the reflection properties of coupled waves at the free boundary are solved numerically and checked by the energy conservation law. The influences of the flexomagnetic effect, strain gradient effect and micro-inertia effect on the wave propagation are discussed. It is found that the flexomagnetic effect mainly enhances the mechanical-magnetic coupled property, strain gradient effect mainly enhances the elastic property, and micro-inertia effect not only enhances the inertia property, but also essentially changes the dispersion characteristics of coupled waves. [ABSTRACT FROM AUTHOR]

In this paper, the coupled linear theory of thermoviscoelasticity for porous materials is considered in which the coupled phenomenon of the following four mechanical principles is proposed: the deformation of the skeleton of a porous solid, the volume fraction concept of the pore network, Darcy's law for the flow of a fluid through a porous medium, and Fourier's law of thermal conduction. The governing systems of equations of motion and steady vibrations are proposed. The fundamental solution of the system of steady vibration equations is presented explicitly by means of elementary functions, and its basic properties are established. By virtue of Green's identity the uniqueness theorems for the classical solutions of the basic internal and external boundary value problems (BVPs) of steady vibrations are proved. Then, the surface and volume potentials are presented and their basic properties are given. Finally, the existence theorems for classical solutions of the above-mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. [ABSTRACT FROM AUTHOR]

In this paper, the stress fields in nonlinear sandwich and laminated composite shells subjected to displacement-dependent loads are analyzed. To solve the problem, the geometrically exact (GeX) hybrid-mixed four-node solid-shell element is proposed. The term GeX means that the middle surface is described by analytical functions, i.e., the parametrization of the surface is known. The laminated solid-shell element formulation is based on the choice of an arbitrary number of sampling surfaces (SaS) parallel to the middle surface and located at the Chebyshev polynomial nodes within the layers, in order to introduce the displacements of these surfaces as unknown functions. The outer surfaces and interfaces are also included into a set of SaS. Due to analytical integration utilized to evaluate the tangent stiffness matrix, the developed GeX solid-shell element under non-conservative loading shows excellent performance in the case of coarse meshes and makes it possible to use only one load step in most of the considered benchmark problems. It is shown that the difference between the second Piola–Kirchhoff and Cauchy stress tensors in some non-conservative problems for sandwich and laminated shells undergoing arbitrarily large rotations can be significant. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration characteristics of stiffened sandwich plates with auxetic core and functionally graded piezoelectric face sheet are investigated. The sandwich plate configuration comprises three distinct layers: a top layer consisting of functionally graded piezoelectric material (FGPie), a core layer composed of auxetic material exhibiting a negative Poisson's ratio, and a bottom layer made of functionally graded material (FGM). The sandwich plate is reinforced by isotropic stiffeners along the x and y directions. A novel model is established based on the four-variable shear deformation refined plate theory and the pb2-Ritz method. This model offers the flexibility to analyze plates with diverse mechanical boundary conditions and supports two types of electrical boundary conditions: closed circuit and open circuit. The accuracy and convergence of the proposed model are validated through comparative analyses against published results, thereby confirming the reliability when analyzing the vibration characteristics of this complex sandwich structure. Furthermore, some new investigations are carried out to explore the influence of various parameters on the vibrational characteristics of the stiffened piezoelectric auxetic sandwich (SA-FGPie) plates. The results suggest that the properties of the reinforcing stiffeners, such as quantity or dimensions, alter the free vibration characteristics of the SA-FGPie plates significantly. In addition, parameters such as the volume fraction indexes of the FGPie and FGM layers, electrical boundary conditions or FGPie layer thickness, as well as geometric parameters of the auxetic unit cell also have a significant influence on the vibration response of SA-FGPie plates. However, the influence of these parameters depends on the specific boundary conditions. [ABSTRACT FROM AUTHOR]

The frictionless contact problem between a conducting triangular or cylindrical punch and a thermoelectric strip is analyzed in this paper. When designing and optimizing thermoelectric devices for energy harvesting and temperature control applications, the interaction between the punch geometry and the thermoelectric strip is crucial. By the Fourier transform, the considered contact problem is formulated as a Cauchy singular integral equation, which is numerically solved using the collocation method. Distinct singular features at the ends of the punch lead to specific collocation methods adopted. A detailed study on various geometrical and loading parameters, including the punch shape and geometry and the thermoelectric loads, is performed, to assess their influences on the mechanical load-contact size curves and the distribution of the normal contact stress. Numerical results demonstrate that it is feasible to reduce the normal contact stress by increasing the thickness of the thermoelectric strip, enlarging the radius of the cylindrical punch, and decreasing the slope of the triangular punch. For both punch types, the deviation of the normal contact stress under the thermoelectric loads from that without the thermoelectric loads exceeds 5%. Hence, when dealing with the contact problem of the thermoelectric materials and structures, it is necessary to account for the impact of the thermoelectric fields on the elastic mechanical field. The findings from the present study may contribute to the further development of more efficient thermoelectric systems. [ABSTRACT FROM AUTHOR]

This paper develops a frictional moving contact model for a functionally graded (FG) orthotropic layer pressed by a rigid cylindrical punch. The FG orthotropic layer is fully bonded to the isotropic half-plane. The punch moves to the left on the layer at a constant subsonic velocity and a shear stress arises in the contact zone according to the Coulomb friction law. General expressions of displacements and stresses are derived with the help of the Fourier transform and Galilean transformation. Using boundary conditions, the moving contact problem is reduced to a Cauchy-type singular integral equation, the unknowns of which are contact stress and contact width. Gauss–Jacobi integration formula is used to solve the obtained singular integral equation. The effect of some parameters and material properties on the contact width, contact stress and in-plane stress are given in graphical forms and detailed numerical interpretations are presented. [ABSTRACT FROM AUTHOR]

Compared to the first-order shear deformation theory and other classical shell theories, the higher-order shear theory is deemed more accurate due to its superior ability to capture transverse shear effects, especially vital for precision in modeling thicker, doubly curved shell panels. Additionally, the third-order shear deformation theory (TSDT) is acknowledged for its computational efficiency compared to the 3D solution striking a balance between result precision and computational efficiency. This paper explores the static bending and free vibration analysis of a porous bi-directional functionally graded doubly curved sandwich shell. For the first time, a combination of TSDT theory with the p-version finite element method is applied, demonstrated for the analysis of bi-directional functionally graded doubly curved sandwich shell. In the initial phase, the mathematical formulation has been meticulously derived. Four models of sandwich FGM distributions, taking into account the porosity effect and comprising a blend of two ceramic materials and a metallic material, have been thoroughly explored. Subsequently, the study evaluates the effectiveness and accuracy of the formulation implemented in FORTRAN CODE through benchmark results, showcasing its adaptability for different shell panel geometries by adjusting the values of the radius of curvature. The latter part of the research delves into new findings related to bi-directional functionally graded porous sandwich FGM shell panels, investigating the effects of gradient indexes and porosity distribution on their behavior. [ABSTRACT FROM AUTHOR]

The objective of this research is to investigate nonlinear elastic foundation effects on the damping characteristics and forced vibrations of sandwich beam, in which a viscoelastic layer is positioned between two identical elastic layers. The analytical formulation takes into account both normal and shear deformations in the core by employing the interlaminar continuous shear stress Zig–Zag Theories (IC-ZZT). The coupling of geometric nonlinearity results in a nonlinear frequency–amplitude equation, which is influenced by several complex coefficients. The paper's first section focuses on determining the linear and nonlinear damping parameters for laminated composite beams. In the second part, a nonlinear forced vibration analysis is conducted, considering both small and large vibration amplitudes. Results show that the nonlinear elastic foundation coefficients have a significant effect on the damping and nonlinear vibration response of sandwich beams. [ABSTRACT FROM AUTHOR]

This paper plans to propose a general numerical model for investigating the free and forced vibration behaviors of the multi-stepped functionally graded porous graphene platelet-reinforced composite (FGP-GPLRC) curved beam with various boundary conditions based on the first-order shear deformation Timoshenko beam theory by employing Rayleigh–Ritz method in conjunction with Jacobi polynomials. Different porosity and GPL distribution types are considered. The general boundary conditions of the multi-stepped FGP-GPLRC curved beam and connecting conditions of the FGP-GPLRC curved beam elements are simulated by employing boundary springs and connecting springs, respectively. The convergence and validation of the proposed numerical model are demonstrated by comparing the proposed results with the corresponding results which come from open literature and finite element software ABAQUS. The free and forced vibration behavior analysis of multi-stepped FGP-GPLRC curved beam is carried out by investigating the influences of material property and geometric parameters on the natural frequency and displacement response in the frequency and time domains of multi-stepped FGP-GPLRC curved beam structure. The investigation results can offer the technique guidance for the design and manufacture of the multi-stepped FGP-GPLRC curved beam. [ABSTRACT FROM AUTHOR]

Micrometeoroids and Orbital Debris (MMOD) travelling at extremely high velocities in space are a threat to the structural integrity of spacecrafts in the Low Earth Orbit. Whipple shield, consisting of a Bumper and a Rear Wall, with a stand-off distance in between, is widely used to protect spacecrafts from hypervelocity MMOD impacts. In this paper, we present numerical simulations of a set of well-known hypervelocity impact (HVI) experiments on aluminium-based Whipple shields reported in the literature. These simulations are conducted using the three-dimensional Lagrangian Finite Element Method in ABAQUS/Explicit software. In six out of the seven tests reported in the literature, the Whipple shield failed due to a detached spall from the back surface of the Rear Wall, while in the seventh test, the spall was not detached. The present work successfully replicates and favourably compares the failure mechanisms observed in these Whipple shields to the corresponding experimental results. Various critical aspects of the Whipple shield's failure mechanics and mechanisms are investigated. These include impact pressure on the projectile, Bumper and Rear Wall, Bumper hole diameter, temperature rise, and residual velocity of debris particles and spalled fragments. The predicted ballistic limit of the Whipple shield falls between 2.54 mm and 3.18 mm of Rear Wall thickness in excellent agreement with the experimental results reported in the literature. The present work provides valuable insights into Whipple shield performance. The developed methodology could be employed to optimize shield design through predictive simulations, thereby improving spacecraft protection. [ABSTRACT FROM AUTHOR]

In this paper, the problem of a V-notch with complex boundary conditions in a piezoelectric/piezomagnetic bi-material strip is studied. Firstly, SH guided wave is considered as an external load acting on piezoelectric/piezomagnetic bi-material strip, on the basis of repeated image superposition, the analytical expression of scattering wave is conducted, which satisfies the boundary conditions on the upper and lower horizontal boundaries of the strip. Then, the analytical expression of standing wave is established, which satisfies the stress-free, electric insulation and magnetic insulation conditions on the boundaries of V-notch by the fractional Bessel function expansion method and Graf addition theorem. Finally, Green's function method is applied, the bi-material strip is divided into two parts along the vertical interface, a pair of in-plane electric field, in-plane magnetic field and out-of-plane forces are applied on the vertical interface, and the first kind of Fredholm integral equations are set up and solved by applying orthogonal function expansion technique and effective truncation. Results clarified the influence on the dynamic stress concentration factor, electric field intensity concentration factor and magnetic field intensity concentration factor under proper conditions. Besides, the analytical solutions are compared with the finite element solutions to verify the accuracy of the conclusions in this article. [ABSTRACT FROM AUTHOR]

Anode materials are a key part of lithium-ion batteries, of which silicon-based anodes are considered the most promising electrode materials due to their high theoretical specific capacity. However, during the operation of the battery, the silicon material undergoes a huge volume change resulting in damage to the electrodes. Currently, the use of additive particles to make composite electrodes is a more reasonable approach. During the charge/discharge cycle of the battery, the electrodes may undergo cyclic expansion/contraction and may undergo elastic deformation and inelastic deformation, and lead to electrode ratchet deformation and capacity degradation. In this paper, a coupled nanoelectrode mechanics-electrochemistry model is developed to investigate the electrode stress evolution and strain accumulation of nanocomposite negative electrode during charge/discharge cycling under different influencing factors, and to analyze the change of electrochemical properties due to diffusion stress. Our work shows that the use of composite matrix materials, on the other hand, exhibits better mechanical stability, has smaller inelastic strains after a cycle, and produces less accumulation of irreversible strains. The established analytical model of nanocomposite electrode helps electrode design and is instructive for the preparation and structural design of nanocomposite negative electrodes. [ABSTRACT FROM AUTHOR]

The propagation characteristics of elastic waves in polycrystalline materials depend not only on grain size, but also on grain size distribution. In this paper, based on Weaver's polycrystalline scattering model, two grain size distribution models, namely the truncated lognormal distribution and the fractal distribution based on fractal dimension, are considered. At the same time, the ultrasonic attenuation of polycrystalline materials is studied by considering the existence of finite interval of grain size. The grain size of the classical lognormal distribution ranges from zero to infinity, which is inconsistent with the actual situation. The present work modifies Turner's study based on the lognormal distribution and compares the numerical results with Turner's. The numerical results obtained from the two kinds of distributions show that the scattering attenuation in the Rayleigh scattering region is affected by both the grain size distribution and the average grain size. In the transition scattering region, the attenuation of P-wave scattering is related to the average grain size and size distribution, while the attenuation of S-wave scattering is mainly affected by the average grain size. In the stochastic scattering region, the scattering attenuation is mainly affected by the average grain size and is not sensitive to the grain size distribution. Moreover, the numerical results also show that the difference of scattering attenuation due to the grain size distribution is most obvious in the Rayleigh scattering region. [ABSTRACT FROM AUTHOR]

By using an effective theoretical model, efficiency and accuracy of design for laminated plates can be significantly improved. However, the existing five-variable higher-order models will encounter difficulty to accurately produce interlaminar stresses, which will influence evaluation on interlaminar performance of laminated plates. Thus, this paper attempts to propose an efficient higher-order model with five variables, where the Legendre polynomial is introduced into in-plane displacement field at each layer. By enhancing compatible condition of displacements and equilibrium condition of stresses, the unknowns depending on the layer number have been eliminated. Differing from other existing five-variable higher-order models, the proposed model can describe the zig-zag effect of in-plane displacements, and fulfill continuity of transverse shear stresses at interfaces. The governing equations are further derived through the principle of virtual displacement, and analytical solutions for only simply-supported plates have been presented. To assess the capability of the proposed method, three-dimensional elasticity solutions have been employed for comparison, and other five-variable higher-order models from the literature have been also chosen for assessment. Numerical results show that the proposed model possesses the same computational efficiency as the selected five-variable models, but can predict more accurate results. In addition, the proposed model is employed to analyze bending behaviors of sandwich and composite plates, and accurate results can be also acquired. Therefore, the present model is proposed to design laminated plates. [ABSTRACT FROM AUTHOR]

Vibration isolation is crucial for scientific instruments that require precise measurements and are highly sensitive to disturbances, especially in microgravity environments, such as ultracold atom interferometry and electrostatic space accelerometers. To minimize micro-oscillations at low frequencies, attention has been drawn toward isolators with quasi-zero stiffness (QZS) and nonlinear properties. Specifically, structures such as curved beams or thin-walled domes that exhibit the potential for elastic buckling have emerged as promising candidates for creating QZS isolators, in contrast to conventional approaches that rely on combining springs with positive and negative stiffness in a larger occupied volume. The idea of mechanical metamaterials, featuring programmable properties, presents a novel approach to achieving QZS characteristics. This paper introduces a new mechanical metamaterial design that arranges QZS units in a Cartesian pattern using curved beams and establishes the dynamic model under base excitation. Initially, the QZS unit, based on a Euler beam with a cosine configuration, is modeled and the analytical force–displacement relationship is constructed by controlling buckling only at low-order modes. The dynamic response of a single QZS unit is analyzed using the harmonic balance method. Subsequently, periodic metastructures with both horizontal and vertical patterns are created and the geometric parameters and overall response of the QZS metamaterials are evaluated. The impact of structural damping, excitation amplitude, and prescribed displacement on the transmission characteristics is also examined. Validation of the analytical results is carried out using the finite element method. In conclusion, this work presents a novel approach to designing QZS vibration isolators that utilize elastic buckling structures for achieving low-frequency isolation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the damped nonlinear vibration of cracked functionally graded (FG) graphene platelets (GPLs)-reinforced composite (FG-GPLRC) dielectric beam. The effective material properties of the composites are evaluated by effective medium theory (EMT) and rule of mixture. Governing equations incorporating damping and dielectric properties are derived from an energy method with the framework of Timoshenko beam theory and nonlinear von Kármán strain–displacement relationship. Stress intensity factor (SIF) of cracked FG-GPLRC beam at the crack tip is obtained via finite element method (FEM). Differential quadrature (DQ) and direct iterated methods are utilized to discretize and solve the nonlinear system. Accuracy and convergence of the model and the solution are verified. An extensive numerical study is performed to examine the effects of crack location and depth, damping and attributes of GPL and the applied electric field on the nonlinear vibration behavior of the cracked FG-GPLRC beam. It is found that the frequency ratios of cracked FG-GPLRC beams are more sensitive to the applied electric field when the crack with larger depth is located close to the mid-span. The cracked FG-GPLRC beams with FG distribution profiles exhibit better stability. [ABSTRACT FROM AUTHOR]

This paper presents an analytical formulation to investigate functionally graded porous beams' nonlinear thermal buckling performance under various boundary conditions. The current model incorporates innovative cinematic techniques with the focus on the stretching effect and the iteration techniques. The material properties of the porous FG beams are temperature-dependent and vary according to a simple power-law distribution. The validity of the present theory' results is confirmed by comparing them with those obtained by other researchers. The findings demonstrate that the critical buckling temperature in TD and TID ranges from 1.03 to 1.27% for a uniform distribution and 1 to 1.47% for linear and non-linear distributions. Conversely, for regular porosity variation, the critical buckling temperatures fluctuate between 0.99 and 1.74%, and between 0.99 and 1.59% for porosity variation. Furthermore, the influence of boundary conditions becomes more pronounced when the nonlinear temperature difference is high. [ABSTRACT FROM AUTHOR]

To perform the accurate and efficient dynamic load identification (DLI) on time-varying (TV) structural systems, this paper proposes a novel time-domain dynamic load identification method, which we call the inverse Wentzel–Kramers–Brillouin (WKB) real function recursive solution. The proposed method can identify the dynamic loads of TV structural systems with different masses, damping, and stiffness online. Based on the WKB real function recursive solution, we first derive the acceleration recursive solution for linear time-varying (LTV) dynamic systems. Then, by reversing the acceleration recursive solution, we obtain the recursive formula for the dynamic load as a function of time. At each time step, this method performs recursion using the load and response of the previous time step to derive the current load. Finally, we demonstrate through numerical simulations that this algorithm has higher identification accuracy and computational efficiency than the inverse Wilson-θ method, and reduces the computation time significantly. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to examine the free vibration behaviors of functionally graded nanobeams with porosity while considering nonlocal parameters. The nanobeams are built of functionally graded materials, having material features that change smoothly over the beam's thickness. To illustrate how porosity is distributed throughout the body of the beams, four different forms of porosity distribution are taken into consideration. Eringen's nonlocal parameter elasticity theory and Hamilton's principle are used to establish the governing equations of the motion of the functionally graded porous nanobeams. Then, the closed-form solution of Navier is used to solve the eigenvalue problems to find the frequencies of the functionally graded porous nanobeams. A comprehensive parametric study is also carried out to demonstrate the influence of geometric parameters, material gradient index, and nonlocal parameters on low- and high-frequency vibration behaviors of the functionally graded porous nanobeams. The results of the vibration of the functionally graded porous nanobeams undergoing the low- and high-frequency conditions can serve as benchmarks for applications of such structures in engineering and for future work. [ABSTRACT FROM AUTHOR]

Nanocomposites have gained fame due to their characteristics and are used in many industries such as automotive, aerospace, and biomedical. Also, curled structures (arches) are deeply applicable in fields of engineering. So, in this paper, the influence of nanoparticles' aggregation on the behavior of the dispersed elastic waves in the hybrid nanocomposite arches is evaluated for the first time. The arches are supposed to be made of hybrid multi-scale nanocomposite reinforced with single-walled carbon nanotubes and carbon fibers. The physical properties of arches are calculated in the framework of the rule of the mixture and the Eshelby–Mori–Tanaka homogenization model. The theoretical formulation of kinetic relations of the arches is presented based on the Euler–Bernoulli curved beam theory. Moreover, Hamilton's principle is applied to obtain the partial differential governing equations of arches. In the next step, an analytical solution method is implemented to solve the derived partial differential equations, and then, the frequency and velocity of the dispersed waves will be calculated. Next, the impacts of different effective parameters on the change of wave dispersion of hybrid nanocomposite arches are comprehensively studied. Finally, the obtained outcomes are reported in detail namely the correlations between phase velocity, wave frequency, weight fraction, etc. [ABSTRACT FROM AUTHOR]