Search

In this study, free vibration of stepped beam which is parallel to a uniform beam with same length and elastically connected to it, is considered. Euler-Bernoulli beam theory has been applied to drive equations of motion, abrupt change in height of beam considered as step and Winkler-type elastic layer model serve as connection between beams. The differential transform method (DTM) is applied to determine dimensionless frequencies and mode shapes. In the case of two uniform parallel beams accuracy of solution is verified by comparing with results reported by other methods. It is assumed all supports have one type and fully clamped and fully hinged supports considered for boundary conditions. The effects of different parameters such as: step location and ratio, connecting layer coefficient and boundary conditions on dimensionless frequencies and mode shapes investigated and discussed. This problem handled for first time in present study and results are completely new. [ABSTRACT FROM AUTHOR]

Purpose: The feasibility of harvesting electrical energy from mechanical vibration is demonstrated in the thesis. In the technique, energy is harvested from simply supported beam vibration under a moving mass using a thin piezoelectric material. Design/methodology/approach: The structure is represented by a basic beam of length L that is supported at both ends and traversed by a moving mass M travelling at a constant velocity v. The Euler-Bernoulli differential equation describes its behaviour. The dynamic analysis of a beam is performed by using three moving masses of (35.61, 65.81, and 79.41) gr each travelling three uniform speeds of (1.6, 2 and 2.4) m/s. A differential equation of the electromechanical system is obtained by transforming the piezoelectric constitutive equation and solved numerically by MATLAB. Findings: The results indicate that the numerical and experimental values for the midpoint deflection of the beam and the piezoelectric voltage are very close. Research limitations/implications: Using the COMSOL programme, the proposed approach is checked by comparing results with data obtained by the finite element method (FEM). An experimental setup was also built and constructed to determine the voltage created by the piezoelectric patch and the beam response as a result of the mass travelling along the beam. Practical implications: The results show that the dynamic deflection, piezoelectric voltage, and piezoelectric energy harvesting all increase as the speed and magnitude of the moving mass increase. The harvesting power vs. load resistance curve begins at zero, increases to a maximum value, and then remains almost constant as the resistance is increased further. The optimal length of the piezoelectric patch was obtained to be 0.63 m. When the length of the beam increases, the resonant frequency decreases, and at the same time the harvested energy increases. However, increasing the beam thickness has the opposite effect; whereas raising the beam width does not affect the resonant frequency but decreases energy harvesting. Originality/value: The most essential point here is the need to have correctly built scale models. They can provide a substantial amount of information at a low cost, accommodate a variety of test settings, and aid in the selection and verification of the most effective analytical model to resolve the actual issue. [ABSTRACT FROM AUTHOR]

A new type of self-oscillating system has been developed with the potential to expand its applications in fields such as biomedical engineering, advanced robotics, rescue operations, and military industries. This system is capable of sustaining its own motion by absorbing energy from the stable external environment without the need for an additional controller. The existing self-sustained oscillatory systems are relatively complex in structure and difficult to fabricate and control, thus limited in their implementation in practical and complex scenarios. In this paper, we creatively propose a novel light-powered liquid crystal elastomer (LCE) fiber-cantilever system that can perform self-sustained oscillation under steady illumination. Considering the well-established LCE dynamic model, beam theory, and deflection formula, the control equations for the self-oscillating system are derived to theoretically study the dynamics of self-vibration. The LCE fiber-cantilever system under steady illumination is found to exhibit two motion regimes, namely, the static and self-vibration regimes. The positive work done by the tension of the light-powered LCE fiber provides some compensation against the structural resistance from cantilever and the air damping. In addition, the influences of system parameters on self-vibration amplitude and frequency are also studied. The newly constructed light-powered LCE fiber-cantilever system in this paper has a simple structure, easy assembly/disassembly, easy preparation, and strong expandability as a one-dimensional fiber-based system. It is expected to meet the application requirements of practical complex scenarios and has important application value in fields such as autonomous robots, energy harvesters, autonomous separators, sensors, mechanical logic devices, and biomimetic design. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the dynamic behaviour of continuously reinforced concrete pavement (CRCP) on a multi‐layered transversely isotropic saturated subgrade subjected to a moving load. The stress‐strain relationship of the CRCP is obtained based on classic lamination theory. Then, the differential governing equations of the pavement are established by D'Alembert's principle. Combining the Fourier series expansion and integral transform technique, the displacements of the CRCP in the wavenumber domain are derived. By introducing pavement‐subgrade interface conditions, the solution to the pavement‐subgrade system is acquired with the use of the extended precise integration method (PIM). The solution in the spatial domain is further obtained by the numerical inverse transform. The presented method and the corresponding program are verified. Finally, parametric studies are conducted to determine the effects of the reinforcement ratio and position, the load velocity and the subgrade stiffness. [ABSTRACT FROM AUTHOR]

This study aims to investigate the elastic–plastic response of a clamped-clamped beam struck by a rigid heavy mass with a low velocity at any point on the span. The impact system is simplified as a single-degree-of-freedom (SDoF) mass-spring model to formulate the beam's equations of motion during loading and unloading. With the consideration of material elasticity and large deflection, elastic–plastic analytical solutions are derived to predict the global deformation behavior of the beam. Validation and comparison are conducted against numerical simulations performed using ABAQUS, and satisfactory agreement is achieved for the predictions of the structural dynamic behavior. Meanwhile, a parametric study is presented to assess the influence of the impact location on the characteristic response parameters, which suggests that the structural stiffness increases as the impact location approaches the beam's support. The findings drawn from analytical and numerical studies can be useful in the anti-impact design of engineering structures. [ABSTRACT FROM AUTHOR]

This study presents a static analysis and natural frequency analysis of functionally graded laminated piezoelectric beams based on the Euler–Bernoulli theory using the finite element method. A simple power law is used to vary all material properties across the thickness, except for Poisson's ratio. The effect of laminate configuration and volume fraction index on the deflection and natural frequency of beams made of functionally graded piezoelectric materials (FGPM) is investigated, and the relationship between deflection and different volume fraction indices under thermal, electrical, and mechanical loads is explored. The study shows that there is a certain volume fraction index that maximizes or minimizes deflection. Additionally, the variation of natural frequency in relation to the power law index is examined. The findings of this research are useful for the development of sensors and actuators in different environments, and the appropriate operation point of the structure can be selected based on the behavior of the sensor or actuator of the beam. [ABSTRACT FROM AUTHOR]

This article deals with the linear and nonlinear buckling behavior of porosity-dependent functionally graded (FG) non-uniform microtubes. The modified couple stress theory is determined to consider small-scale effects on the micro-size tube which is modeled, based on the Euler–Bernoulli beam theory in conjunction with the employment of the conservation energy principle to derive the nonlinear governing equations regarding the nonlinear Von-Kármán strains. The main contribution of this article is the impact of cross-sections on the static behavior of cylindrical beams with four applicable cross-sections, involving the exponential, linear, and convex in comparison of uniform section for the radial distribution of ceramic and metal material based on the power-law function. Also, the pinned, clamped, and combination of these boundary conditions are defined as the boundary supports, and the generalized quadrature method (GDQM) is utilized as the numerical solving technique along with the iteration method to solve the nonlinear equations. Finally, the obtained results extracted to investigate the impact of various parameters, involving the nonlinear amplitude, power FG index, porosity parameter, small-scale parameter, and different cross-sections on the buckling treatment of cylindrical beam. [ABSTRACT FROM AUTHOR]

Based on the Euler–Bernoulli beam element theory, a nonlinear finite element method is proposed to solve the mechanical response of functionally graded shape memory alloys (FG-SMAs) three-point bending beam considering the tension–compression asymmetry under the loading process. The Auricchio's shape memory alloy (SMA) constitutive model was used to describe the phase transformation relationship of SMA. The constitutive model of the power exponent distribution law of FG-SMA was developed by using the theory of composite mechanics. Using the virtual work principle, the bending beam equilibrium equation of FG-SMA was developed. The finite element method and Newton–Raphson method were used to solve the equilibrium equation of the three-point bending beam of FG-SMA. The accuracy of the proposed method was verified by comparing the present results obtained by the nonlinear finite element method with the existing literature. Then three-point bending beam analysis of FG-SMA was carried out. The results show that the increase in the graded index and tensile asymmetry coefficient increases the stiffness of the beam. When the SMA enters phase transformation, the increase in temperature will reduce the deflection of the beam. In addition, the strain variation in the mid-span section near pure shape memory alloy layer is more obvious than that near pure ceramic layer due to temperature. The compressive axial load is more likely to cause beam bending than tensile axial load. [ABSTRACT FROM AUTHOR]

In this paper, two types of fractional-order damping are proposed for a single flexible link: internal and external friction, related to the material of the link and the environment, respectively. Considering these dampings, the Laplace transform is used to obtain the exact model of a slewing flexible link by means of the Euler–Bernoulli beam theory. The model obtained is used in a sensing antenna with the aim of accurately describing its dynamic behavior, thanks to the incorporation of the mentioned damping models. Therefore, experimental data are used to identify the damping phenomena of this system in the frequency domain. Welch's method is employed to estimate the experimental frequency responses. To determine the best damping model for the sensing antenna, a cost function with two weighting forms is minimized for different model structures (i.e., with internal and/or external dampings of integer- and/or fractional-order), and their robustness and fitting performance are analyzed. [ABSTRACT FROM AUTHOR]

This paper proposes a method to amplify the performance of a flexural-wave-generation system by utilizing the energy-localization characteristics of a phononic crystal (PnC) with a piezoelectric defect and an analytical approach that accelerates the predictions of such wave-generation performance. The proposed analytical model is based on the Euler-Bernoulli beam theory. The proposed analytical approach, inspired by the transfer matrix and S-parameter methods, is used to perform band-structure and time-harmonic analyses. A comparison of the results of the proposed approach with those of the finite element method validates the high predictive capability and time efficiency of the proposed model. A case study is explored; the results demonstrate an almost ten-fold amplification of the velocity amplitudes of flexural waves leaving at a defect-band frequency, compared with a system without the PnC. Moreover, design guidelines for piezoelectric-defect-introduced PnCs are provided by analyzing the changes in wave-generation performance that arise depending on the defect location. [ABSTRACT FROM AUTHOR]

Energy harvesting from vortex-induced vibrations (VIV) is gaining more attention in many applied cases. This paper studied the nonlinear dynamics of a tunable VIV-based energy harvester. The energy harvester structure consists of a base-clamped cylinder having an adjustable mass (the tuner) which enables the system to actively synchronize with vortex-shedding frequencies. The Euler-Bernoulli beam theory and the extended Hamilton's principle are used to extract the nonlinear partial differential equations of the distributed model for the cylinder, tuner motion, harvested voltage, and fluctuated lift force. The reduced-order model of the system of equations is derived via the Galerkin method using modified mode shapes. The method of multiple time scales is employed to obtain the approximated analytical solution of the 1:1 internal resonance of the lumped parameter system. The dynamical response of the system is shown by investigating various parameters of the harvester. Additionally, the locus of the points at which the higher orbits of harvested voltage occur is specified for the tuner equilibrium position. The results show the proposed design significantly increases energy harvesting performance by a factor of 900%. This paper is offered as a contribution towards energy harvester design and optimization with the goal of capturing higher energy orbits. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The wind and wave loads on the offshore wind-turbine (OWT) structures with monopile foundations occur at specific frequencies. When these excitation frequencies are close to the natural frequencies of OWT structures, resonance can disturb the proper operation of the power-generation equipment and shorten the service life of the structural system. Therefore, to ensure safe and efficient operation, the natural frequencies of the OWT structures with monopile foundations must be determined. To this end, a calculation method for the natural frequencies of the OWT structures with monopile foundations is proposed. This method, which considers the mass ratio (the ratio of the lumped mass on the top of the tower to the total mass of the tower, the transition piece, and the monopile above the mudline) as well as the nonuniform moment of inertia of the structures above the mudline and the soil–structure interaction (SSI), is derived using the Euler–Bernoulli beam differential equation and slope-displacement equation of a monopile according to the flexibility matrix, stiffness equivalent principle, and virtual work principle. Finally, the natural frequency calculation method is compared with finite element simulation and other calculation methods. [ABSTRACT FROM AUTHOR]

Trees have various forms and structures, most of which have excellent mechanical properties. Spruce has a stable structure and excellent resistance to wind and snow loads. In this paper, the vibration performance of spruce is studied by the semi-analytical method. Based on the vibration theory of Euler–Bernoulli beam, the vibration mechanical model of the spruce trunk with variable cross-section is established by using the segmental equivalence method. Then, the natural frequency and modal function of the trunk are analyzed and the displacements are solved under snow load within one hour. The results show that the first four natural frequencies are 120.417 rad/s, 188.414 rad/s, 237.699 rad/s and 288.964 rad/s, respectively. During the continuous loading stage, the displacements increase over time. During the static load stage, the displacements change in a harmonic form. The above results are verified by an experimental measurement. This paper provides a reference for the study of the vibration performance of similar structures. [ABSTRACT FROM AUTHOR]

The harvesting efficiency of a cantilevered piezoelectric energy harvester is limited by its uneven strain distribution. Moreover, a cantilevered harvester requires a large workspace due to the large displacement of its free end. To address these issues, a novel piezoelectric energy harvester based on an extended simply supported beam is proposed. The proposed design features a simply supported piezoelectric main beam with an extended beam attached to its roller end and a tip mass to reduce the resonant frequency. The theoretical model of the proposed piezoelectric energy harvester is developed based on the Euler–Bernoulli beam theory. The model has been experimentally validated through the fabrication of a prototype. The extended beam and tip mass are adjusted to see their influence on the performance of the harvester. The resonant frequency can be maintained by shortening the extended beam and increasing the tip mass simultaneously. A shorter extend beam leads to a more even strain distribution in the piezoelectric layer, resulting in an enhanced output voltage. Moreover, the simulation results show that a torsional spring is installed on the roller joint which greatly influences the voltage output. The strain distribution becomes more even when proper compressive preload is applied on the main beam. Experiments have shown that the proposed design enhances the output power by 86% and reduces tip displacement by 63.2% compared to a traditional cantilevered harvester. [ABSTRACT FROM AUTHOR]

This paper investigates the influence of a circumferential crack on a simply supported beam's free vibration behavior analytically and numerically. The beam is modeled by Euler–Bernoulli beam theory with a circular cross-section. The circumferential crack is modeled by considering a continuous effect in the displacement field. An exponential function is considered in the displacement field with an exponential decay rate parameter which characterizes the influence of crack on its surroundings. The exponential function of crack depth ratio was proposed for the exponential decay rate of symmetric circumferential open cracks using a comparative method based on finite element simulation for the first time. The equation of motion is derived using Hamilton's principle and solved by a Galerkin method, and natural frequencies are obtained. The crack depth and position influence on the natural frequency are analytically clarified and compared with a symmetric and single-edge crack. The possibility of identifying the location and relative depth of the crack has been investigated. Whatever the crack is, closer to the maximum amplitude vibration in each mode, the frequency ratio is more dropped, making it more detectible. Also, the circumferential crack is more affected on vibration behavior than the symmetric and single-edge crack. The analytical results have excellent conformity with the finite element results obtained by the ABAQUS 3-dimensional model. Also, some experimental results have been obtained to validate the finite element model. The finite element model has an excellent agreement with experimental results. The results can be used to identify circumferential cracks. [ABSTRACT FROM AUTHOR]

This paper is concerned with both observability and observers for a class of systems described by the two-dimensional hyperbolic PDEs with superlinear boundary conditions which can exhibit chaos. The exact observability and approximate observability are shown by the method of characteristic and boundary reflection relations. Based on the observability, two Luenberger types of PDE observers are designed by making use of the boundary velocity and boundary displacement measurement, respectively. Some sufficient conditions are then developed to obtain the global exponential stability and global asymptotic stability of the observer error systems. Some numerical simulations are performed to validate the theoretical results. [ABSTRACT FROM AUTHOR]

The free vibration properties of a sandwich beam with axially graded facings and a magnetorheological fluid core are studied. The facings and core are modeled using the Euler–Bernoulli and Timoshenko beam theories, respectively. The problem is discretized using the Rayleigh–Ritz method. The approached complex eigenmodes method is implemented for solving the resulting nonlinear eigenvalue problem numerically. The effects of multiple parameters, i.e., facings' material distribution, functionally graded material's gradient index, boundary conditions, constraining and core layers' thickness, and magnetic field effect on the free vibration properties, are thoroughly studied. The obtained results reveal these parameters' significant impact on the frequency and loss factor of the system. [ABSTRACT FROM AUTHOR]

This work proposes an analytical modelling method for free and forced vibration analyses of a delaminated beam structure based on the Green's function method, which considers the connection among sub-beams to generate a general model of a beam with different delaminations. This analytical modelling allows the investigation on the dynamic response of a delaminated beam under frequency-varying excitations. Two models have been developed, the 'free mode' and 'constrained mode' models, for simulating the dynamic response of a delaminated beam with its solution obtained from utilizing the Green's functions on multiple segments of the beam structure. The accuracy of the proposed models is verified by comparisons of results from the finite element models and the previous works that utilized the classical beam theory, demonstrating consistent dynamic characteristics of a delaminated beam structure. It is found that the delamination location has dominant influences on the deformation of the beam and its natural frequencies, compared to the delamination size and depth, with the higher frequency excitation generally has more influences on beam deformation compared to the low frequency excitation for a particular delamination configuration. The results demonstrated the effectiveness of the proposed modelling method for free and forced vibration analyses of a beam with delamination. [ABSTRACT FROM AUTHOR]

A theory for two-dimensional (2D) beams is presented for the case of considering new constitutive equations, wherein the linearized (infinitesimal) strain tensor is assumed to be a nonlinear function of the Cauchy stress tensor. An incremental formulation is developed to solve numerically the resultant equations. Three constitutive equations for elastic bodies are considered: a model wherein we have strain-limiting behavior, a nonlinear model for rock, and a bimodular constitutive equation for rock (which can also be considered as a nonlinear model for rock). Two boundary value problems are studied: the deformation of a cantilever beam with a point load, and a three-point beam with a point load applied on the middle. The numerical results are compared with the predictions of the classical theory for beams for the case of linearized elastic solids. The results for the stresses can be notoriously different, when comparing the predictions of the nonlinear constitutive equations with the results obtained using the linearized theory of elasticity. [ABSTRACT FROM AUTHOR]

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton's principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function. [ABSTRACT FROM AUTHOR]

In this paper, based on Euler-Bernoulli beam theory, the vibration of a helicopter blade is studied. In this regard, the partial differential equation of motion is obtained and solved for a clamped beam numerically. The aerodynamic forces are introduced in terms of the pilot parameters included the collective pitch, lateral cyclic, longitudinal cyclic, and built-in twist on the blade deformation. Moreover, the effects of the blade rotational angular velocity, flight altitude, the blade length, and induce velocity on the blade deflection are studied. The results show that the blade deformation will be oscillating in terms of time and it is very sensitive to the control parameters, its geometry, and the environmental conditions. Moreover, it is observed that the pilot coefficients have more effect on the blade deformation in comparison with other parameters. [ABSTRACT FROM AUTHOR]

In this work the influence of the interphase region in a three-phase magneto-electro-elastic composite material on the energy harvesting characteristics of a vibration based cantilever beam is studied analytically. The three-phase composite made of Barium Titanate/Terfenol-D/Cobalt Ferrite with different interphase regions have been considered for the evaluation. The mathematical expressions for the coupled governing equations are derived through a lumped parameter model in conjunction with Gauss's Law, Newton's Law and Faraday's Law. The generated electric and magnetic potential are harvested through the surface electrodes and a wound coil. The numerical results suggest that the interphase volume fraction and composition adversely affect the coupled material properties, which in turn significantly alters the output response of the energy harvester. Also, the lower values of resistance and number of turns of coil have a predominant effect on the energy harvester's performance. The results of this work demonstrate the significance of the interphase region and its effects on the coupled energy harvesting behavior in multifunctional composite materials. [ABSTRACT FROM AUTHOR]

• Nonlinear unimorph and bimorph models for cantilever-based FGMEEM energy harvesters are presented. • Analytical perturbation solutions for the free vibration and primary resonance cases are provided. • Several comparisons are made to ensure the accuracy of the introduced models. • The supremacies of the present harvesters especially the bimorph case compared to the conventional FGPM systems are addressed. This paper nonlinearly models cantilever-based functionally graded magneto-electro-elastic energy harvesters (FGMEEEH) for the first time. The coupled magneto-electro-mechanical model is obtained on the basis of the Euler-Bernoulli beam theory. A hybrid procedure including Ritz's method is then utilized to generate reduced order models for both asymmetric unimorph and symmetric bimorph configurations. The resulting sets of initial value problems, whose convergence will be examined, are then analytically solved using the method of multiple time scales for both the free vibrations and primary resonance cases. The analytical time-histories of the system are compared by those obtained numerically and excellent agreements between them are observed. In addition, simplifying the frequency response function of the system in the primary resonance case, the present findings are validated by those available in the literature for linear unimorph systems. The influences of the harvester configurations, base acceleration amplitude, the value of the tip mass, the material gradation index as well as the resistances of the piezoelectric and magnetic circuits on the nonlinear response of the system are also studied in detail. It is observed that FGMEEEEHs enjoy much more efficiency in comparison to piezoelectric-based systems. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic behavior of an infinite beam on layered transversely isotropic (TI) poroelastic media due to moving harmonic loads. Based on the Euler‒Bernoulli beam theory and Biot theory, the governing equations of the beam and the layered TI poroelastic media are established. By introducing the compatibility conditions at the beam‐subgrade interface, the equivalent stiffness of the layered TI saturated media is derived via the extended precise integration method (PIM) in the wavenumber domain. By means of the inverse Fourier transform algorithm, the physical solutions for the beam‐saturated soil system are obtained after introducing the equivalent stiffness. Then, the accuracy of the proposed method is verified. Several numerical examples are presented to discuss the influences of the moving speed, beam bending rigidity, stratification, and soil anisotropy on the dynamic behavior of beams. [ABSTRACT FROM AUTHOR]

In this work, we present a detailed static and dynamic analysis of a recently reported electrically actuated buckled carbon nanotube (CNT) resonator, based on the Euler–Bernoulli beam theory. The system behavior is analyzed using the Galerkin reduced-order model. We present a detailed two-dimensional analysis, which predicts static behavior similar to buckled micro-beams, despite the difference in the force dependency on the beam deflection. However, we show that buckled CNTs are the first type of buckled beams to exhibit out-of-plane static deflection, resulting in a unique three-dimensional snap-through transition, never before predicted. In addition, we show the criteria under which these devices can also exhibit latching phenomena, meaning that they can maintain their buckled configuration when no force is applied, making these devices appealing for mechanical memory applications. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Southeast University / Dongnan Daxue Xuebao is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To design a flexure hinge with high precision and high natural frequency, the sinusoidal flexure hinge is proposed in this article. First, the formulae for the compliance and precision factors of the hinge were derived based on the Euler–Bernoulli beam theory and the Gauss–Legendre quadrature formula. The natural frequency was also investigated based on the transfer matrix method. Compared with the simulation results of ANSYS Workbench, the results show that the modeling error is less than 6.7%. Second, the influence of structural parameters on compliance, precision factor, compliance precision ratio, and natural frequency was analyzed. The results show that compliance and precision are often contradictory, and the minimum thickness significantly influences the hinge's performance. Compared with conic flexure hinges in terms of compliance, precision, compliance precision ratios, and natural frequency, the sinusoidal flexure hinges have a better comprehensive performance. Finally, a flexure hinge was manufactured, and compliance was measured. The experimental results show that the error between the experimental value and the modeling value is 7.8%. Both simulation and experimental results verify the effectiveness of the sinusoidal flexure hinge model. [ABSTRACT FROM AUTHOR]

The authors present an analytical solution for the two-layered composite beams with imperfect shear connections. The considered beam is simply supported at both ends. The beam is subjected to transverse and axial loads. The kinematic assumptions of the Euler-Bernoulli beam theory are used. The connection of the beam components is perfect in normal direction, but the axial displacement field may have jump. The shear axial force derived from the imperfect connection is proportional to the relative slip occurring between the layers. The determination of the analytical solution is based on the Fourier method. Two examples illustrate the application of the presented analytical method. [ABSTRACT FROM AUTHOR]

Copyright of Theoretical & Applied Mechanics is the property of Theoretical & Applied Mechanics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Nano-electro-mechanical systems (NEMS) require perforated beams for structural integrity. Hole sizes, hole numbers, and scale effects need to be modelled appropriately in their design. This paper presents a new finite element model to investigate the modal behaviour of longitudinally perforated nanobeams (LPNBs) using the classical Euler–Bernoulli beam theory. A symmetric array of holes arranged parallel to the length direction of the beam with equal spacing was assumed for the perforation. The non-local Eringen’s differential form was used to incorporate the nanoscale sizes. The accuracy of the proposed model was verified by comparing the obtained results with the available analytical solutions for fully filled nanobeams. The effects of aspect ratios, non-local parameters, boundary conditions, and perforation characteristics on the modal behaviour of LPNBs were investigated. The non-local parameter reduced the natural frequency owing to a decrease in the stiffness of the structures. However, the perforation filling ratio led to higher values of the fundamental frequency. Furthermore, compared with other boundary conditions, clamped–clamped boundary conditions demonstrated the best performance in terms of the maximum frequency.

This paper attaches importance to the design and manufacturing of a type of intelligent boundary for vibration control of the elastic beam structure. Artificially set as 12 working states in this study, the intelligent boundary consists of the executing element and the control element. The equivalent stiffness coefficients of the intelligent boundary under each working state are obtained through the experiment. The study on the influence imposed by the intelligent boundary on the forced vibration responses of the elastic beam structure is carried out through the experiment. Based on this work, the equivalent stiffness of the intelligent boundary can be effectively controlled through the change to its working state. The adjustment to the range for the stiffness coefficients of the intelligent boundary can be conducted by changing the line diameter of the springs. In the effective working region, the change to the working states of the intelligent boundary imposes a significant influence on the vibration responses of the elastic beam structure, where an appropriate working state of the intelligent boundary effectively suppresses the vibration at the boundary of the elastic beam. The intelligent boundary can control the vibration of the elastic beam structure through the change to its boundary condition. The control flow of the intelligent boundary is proposed to improve the engineering acceptance of the intelligent boundary. [ABSTRACT FROM AUTHOR]

The article presents a study which explores the unexpected bending behavior of architected two-dimensional lattice materials. It also explores the mechanisms that lay in the competitive interaction between axial torsion and out-of-plane bending of the beams and can be well captured by a Cosserat continuum model.

This paper studies the free vibration response of a spinning and variable cross-section composite cutter bar homogeneously enhanced with carbon nanomaterials. Based on the Rules of Mixture (ROM) and the Halpin–Tsai Model (HTM), we establish a motion model of the spinning and variable cross-section composite cutter bar by containing carbon nanomaterials, which combines the Euler–Bernoulli beam theory and Hamilton principle. In addition, the dynamic governing equations are solved by using the Galerkin method so as to obtain the characteristic equation. The curves of decay rate-rotating speed and natural frequency-rotating speed are obtained especially by numerical analysis, and the corresponding critical speed and instability threshold of the composite cutter bar are also calculated. By selecting different parameters such as length-to-diameter (or length-to-width-to-thickness) ratios and volume contents of carbon nanomaterials, cutter bar taper ratios, ply orientations, and stacking sequences, the relation between instability threshold and loss factor is obtained with respect to the composite cutter bar. The results obtained found that the cutter bar's stiffness is increased by adding carbon nanomaterials into the carbon fiber-reinforced polymer composites. Its natural frequency and critical speed are increased, but the cutter bar's damping decreases with the increasing content of carbon nanomaterials. The results of critical speed and fundamental natural frequency of composite cutter bar for high-speed machining are greatly meaningful. [ABSTRACT FROM AUTHOR]

This paper presents the nonlinear frequency behavior of cracked functionally graded porous beams subjected to various boundary conditions using Reddy shear deformation theory and Green's tensor together with the Von Karman geometric nonlinearity. The material properties of the beam vary exponentially in thickness direction. A generalized differential quadrature method (GDQM) in conjunction with a direct numerical iteration method is developed to solve the system of equations derived by means of Hamilton's principle. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Euler and Timoshenko beam theory. The results for extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratios, porosity indexes, shear and elastic foundation parameters, and boundary conditions on the nonlinear frequency behavior. The location of crack plays the significant role on the nonlinear frequency ratios. The frequency ratios hit the minimum when the crack is located in mid-span of the beam. In this regard, the effect of shear stiffness of foundation is much more than that of Winkler one in the increasing mid-span value of nonlinear frequency ratio. It is also shown that the crack location results in decline of frequency ratios in the mid-span of beam specially for the cracks located closer to surface, the deeper ones lead to get nonlinear frequency ratios rise much more due to the fact that the deeper the crack is, the weaker the crack section becomes. The results of this paper and the effects of these parameters can be used in the optimal design of functionally graded beams and in crack prediction, detection, and monitoring techniques. [ABSTRACT FROM AUTHOR]

Acoustic Black Hole (ABH) is a power-law taper in beam-plate structures that allows a smooth and progressive diminishing of the bending wave speed, even reduced to zero with no residual thickness. However, despite the use of viscoelastic damping layers, significant annulling of reflected waves only appears in mid-to-high frequency band. By contrast, acoustic metamaterials in local resonant mode can create relatively low-frequency band gaps for wave decay. This paper designs a sandwich beam combining the ABH features with local resonance mechanism to realize the sub-wavelength vibration reduction. To maintain the external shape, we resort to a double-leaf configuration with periodic ABH inclusions. It has been indicated that the newly designed structure opens a lower frequency band gap and wider bandwidth compared to its counterpart which made of only single material. The parametric analysis shows that increasing the ABH power and reducing the truncation thickness could further widen these gaps, while the add-on mass of the viscoelastic layer will benefit to the attenuation intensity. In what concerns the structural strength, stiffeners are inserted to alleviate the stress concentration with negligible modification to the transmission spectra. The results indicate that this approach will prompt the design of broadband acoustic devices at deep sub-wavelength scales and shed light on vibration control. [ABSTRACT FROM AUTHOR]

In this study, the dynamic response of FGM (functionally graded materials) beam with surface effect immersed in fluids under high-frequency photothermal excitation is investigated theoretically. The governing equations of FGM beams are derived under Euler–Bernoulli beam theory. The cubical assumption is adopted to describe stress along thickness of FGM beam. In consideration of photothermal force and hydrodynamic load, the solution of forced vibration is obtained by means of the Fourier series expansion of variables. Theoretical analysis shows that the volume fraction and surface effect have an important influence on the response of beams immersed in different fluids; for the FGM material, an optimal material distribution proportion can maximize the response of beams. Among the parameters of the surface effect, the influence of surface residual is greater than surface elastic modulus and surface density. The influence of fluids on resonant frequencies is much more significant than surface effect. This study can provide some references to the application of micro- and nano-FGM structures in Micro-Electro-Mechanical System and Nano-Electro-Mechanical System. [ABSTRACT FROM AUTHOR]

We are concerned with the dynamic stabilization for a cascaded Euler–Bernoulli beam (EBB) partial differential equation (PDE)–ordinary differential equation (ODE) system subject to boundary control and matched internal uncertainty and external disturbance. State feedback stabilization of such system without disturbance has been recently discussed by X.H. Wu, H. Feng (Sci China Inf Sci, 2022, 65(5): 159202). An infinite‐dimensional disturbance estimator is constructed in order to estimate the total disturbance. By compensating the total disturbance, we design a state observer to trace the state and then an estimated state and estimated total disturbance‐based output feedback control law. It is proved that the original system is exponentially stable, and other states of the closed‐loop are bounded. Some numerical simulations are presented. [ABSTRACT FROM AUTHOR]

In the present study, transverse wave propagation in single-walled and double-walled carbon nanotubes is investigated based on doublet mechanics theory. The Euler–Bernoulli and Timoshenko beam theories are considered to study the wave dispersion relations of single-walled and double-walled carbon nanotubes (CNTs) with the set of relevant governing equations are achieved by use of the variational Hamilton's principle. Obtained governing equations are presented for zigzag and armchair CNT models. Using these models, scale dependent wave frequency, phase velocity and group velocity of CNTs are obtained. It has been observed that doublet mechanics results have so called van Hove singularity. This property is the first seen among the scale-dependent continuum theories. The effectiveness and validity of the present method are approved by comparing the predicted numerical results with molecular dynamics simulation and nonlocal Timoshenko beam theory. An excellent validation is obtained between the doublet mechanics based on Timoshenko beam theory and molecular dynamics simulation for phase velocities of (5,5) and (10,10) armchair single-walled CNTs. Also, this work clarifies the importance of the length scale effect on transverse wave dispersion in multi-walled CNTs. [ABSTRACT FROM AUTHOR]

The idea of transferring vital drugs through nanotubes in the human body has attracted the attention of many researchers in the field of nanomedicine. Accordingly, the main objective of this article is to investigate the forced vibration response of two hybrid smart carbon nanotubes connected using springs and conveying a nanofluid, with each one including either a piezoelectric or electrorheological fluid layer. To this aim, a slip boundary condition along with a Knudsen number is employed to address the vibration behavior of smart hybrid sandwich nanotubes acted upon by a moving sinusoidal load, while equations are derived with the aid of the Timoshenko beam model and nonlocal strain gradient theory. The former theory is complemented with hardening and softening material effects which can greatly enhance the precision of the results. Furthermore, Hamilton's principle is implemented to obtain the equations of motion. Regarding the time response of the structure, a combination of modal analysis and the Laplace transform is applied. The accuracy of the developed procedure is verified through a set of comparisons of static deflection (as a result of a point load) and vibration frequencies. In addition, the impact of a number of parameters ranging from nanoparticle velocity to material length scale is investigated. [ABSTRACT FROM AUTHOR]

• The local flexibility matrix of the inclined cracked functionally graded material (FGM) beam is studied and validated. • The bending and tensile stiffnesses of the inclined cracks and their interaction are taken into consideration. • The vibrations of the FGM beam with multiple inclined cracks are investigated. • The wave propagation characteristics of the cracked FGM beam are presented. This paper proposes an FEA method to study the vibration and wave propagation in functionally graded material (FGM) beams with multiple inclined cracks by introducing the local flexibility matrix caused by the cracks. The bending and tensile stiffnesses of the inclined cracks and their interaction are taken into consideration. Two-node (three degrees of freedom per node) beam element is used. The inclined cracks are equivalent to transversal cracks to calculate the additional flexibility matrix of the inclined cracked FGM beam element. The material properties of the FGM beam are supposed to satisfy the exponential law along its thickness. The governing equations of motion for the FGM beam with multiple inclined cracks are deduced in the frame of Euler-Bernoulli theory and Lagrange function, and numerically solved by the Newmark average acceleration method. Both theoretical and numerical comparisons are presented to validate the present method for the inclined cracked FGM beam with varying boundary conditions, arbitrary inclined crack angles as well as varying inclined crack lengths. The effects of the location, length, inclined angle and number of the inclined cracks as well as material property ratio on the fundamental frequencies and wave propagation characteristics of the inclined cracked cantilever FGM beams are comprehensively investigated. [ABSTRACT FROM AUTHOR]

A nonlinear MEMS multimass sensor is numerically investigated, designed as a single input-single output (SISO) system consisting of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is constrained by a linear spring and a dashpot. The microcantilevers are made of a nanostructured material, a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT). The linear as well as the nonlinear detection capabilities of the device are explored by computing the shifts of the frequency response peaks caused by the mass deposition onto one or more microcantilever tips. The frequency response curves of the device are obtained by a pathfollowing algorithm applied to the reduced-order model of the system. The microcantilevers are described by a nonlinear Euler-Bernoulli inextensible beam theory, which is enriched by a meso-scale constitutive law of the nanocomposite. In particular, the microcantilever constitutive law depends on the CNT volume fraction suitably used for each cantilever to tune the frequency bandwidth of the whole device. Through an extensive numerical campaign, the mass sensor sensitivity estimated in the linear and nonlinear dynamic range shows that, for relatively large displacements, the accuracy of the added mass detectability can be improved due to the larger nonlinear frequency shifts at resonance (up to 12%). [ABSTRACT FROM AUTHOR]

An exact analytical solution, in terms of Bessel functions, was derived for the dynamic response of a shear beam with uniform cross section and mass density, and shear modulus that varies exponentially in the axial direction. The solution was generalized to a chain of such beam elements. The model may be appropriate for frame structures, which deform predominantly in shear, with gradually increasing rigidity toward the base. The results of a parametric study are presented for the frequencies of vibration and their ratios, mode shapes, transfer functions, and impulse response functions. The gradation affected the ratios between the frequencies of the higher modes of vibration and that of the fundamental mode, which were smaller than the corresponding ratios for a homogeneous shear beam and were progressively smaller for larger gradation constants. The mode shapes and the ratios of the amplitudes of the pulses in impulse response functions had amplitude amplification toward the top, which was larger for larger gradation constants, and suggests trapping of energy in the upper part of the structure. This effect may be responsible for observed damages and failure of structures in parts far from the base. The gradation also affected the symmetry and shape of the pulses in impulse response functions. The results of the parametric study may be useful for interpretation of the seismic response of full-scale structures. The model is intended for use as a simple surrogate model in structural system identification and health monitoring of frame structures. [ABSTRACT FROM AUTHOR]

This article presents large deflection data for prismatic (unvarying cross section across length) and non-prismatic (tapered, i.e. varying cross section across length) cantilever beams subjected to concentrated tip loads using the finite element method for different taper ratios. The approximate nonlinear solution is derived from the perspective of a polynomial function. The tapered beams that correlate to the nonprismatic cantilever beams have different widths, depths, and diameters. Using the aforementioned large displacement data that have been analysed, a very simple approach is used to evaluate the large amplitude first mode frequency for the cantilever beam with (nonprismatic) tapered and without (prismatic) tapered. The current approach can be used effectively to find accurate results with far less computer capacity as compared to other methods available in the literature. The difference between the current findings and the bibliographic data is shown. The major goal of this work is to contribute to the simple description of polynomial functions for large amplitude first mode free vibration frequency problems with and without tapered beams in terms load parameter(𝜆) versus tip slope (𝛼)and tip amplitude(𝑎/𝐿). Large amplitude first mode frequency (𝛺) increases with tip slope(𝛼). This indicates that the prismatic and non-prismatic cantilever beams exhibit hardening type nonlinearity. At a particular tip slope(𝛼), the diameter taper shows higher frequency than other tapered beams and uniform beams. According to current studies, it can be restricted to a lower range of tip slope(𝛼)or amplitude(𝑎/𝐿). [ABSTRACT FROM AUTHOR]

Dynamic interaction between train wheel and high-speed slab is an important issue when evaluating the contact force at the wheel–rail interface under the influence of an irregularity either on the train wheel or on the rail. In this paper, an influence of amplitude of irregularity along with the vehicle speed on the dynamics of wheel–rail interaction for high-speed railway tracks is being analyzed. For this purpose, single-wheel high-speed railway (HSR) track interaction models are developed using the bond graph modeling technique. The HSR track model consists of two layers of beam, i.e., rail and concrete slab. Both the rail and slab track is modeled using the Euler–Bernoulli beam theory. The Hertzian contact theory at the wheel–rail interface has been considered for this analysis. The vertical dynamic interaction between a train wheel and a high-speed slab track is compiled in the time domain using a bond graph approach coupled with a technique known as modal superposition. Irregularity present on the wheel is characterized as smooth, moderate, and severe depending upon the variation of irregularity amplitude. An expeditious increase of maximum contact force has been observed between the speed range of 200 and 250 km/h. Beyond the speed of 250 km/h, there is a gradual increment of contact force up to its peak value. When the train speed is beyond 288 km/h, there is a gradual decrease in maximum contact force. This kind of several other useful dynamic responses in terms of wheel acceleration and wheel–rail overlap are also evaluated. [ABSTRACT FROM AUTHOR]

This work is dedicated to the study of shear vibration modes of one‐dimensional granular microstructured beams using a discrete Cosserat model. The dynamic response of the one‐dimensional granular beam (discrete beam) is investigated for various boundary conditions, through the analytical resolution of an exact discrete eigenvalue problem. For an infinite number of grains, the dynamic behavior of the discrete problem converges towards a Bresse–Timoshenko continuum beam model. First, the effective modeling parameters, the constitutive equations and the governing equations of motion are derived in a difference form. For simply supported granular beams, the appearance of pure shear modes of vibration is highlighted (vibration modes without deflection), a phenomenon which is already known in the free vibration of a continuous Bresse–Timoshenko beam problem. The eigenfrequencies of these pure shear modes for the discrete granular beam coincide with the critical frequencies of the discrete system. These pure shear modes may appear for granular beams composed of few grains, which give a physical support of a phenomenon well studied in the literature from a continuum beam model. The eigenfrequencies of the discrete granular beam are also calculated for various boundary conditions, including clamped, hinge and free end boundary conditions. Based on the discrete element method (DEM), several numerical simulations of dynamic tests in some representative examples have been performed. The responses of the numerical approach are accurately compared against the exact results of the analytical solutions based on the difference eigenvalue problem, which illustrates the relevance of the proposed approach. [ABSTRACT FROM AUTHOR]