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The accurate representation of real floor behavior is crucial for assessing human-induced vibration serviceability. Many researchers focus on developing computational models and field testing to reflect actual serviceability conditions. Although traditional boundary conditions are commonly used, limited attention has been given to optimizing these conditions. To begin with, this paper introduced semirigid boundary conditions into a finite-element model of the floor and optimized physical parameters and boundary constraint stiffness using the simulated annealing-particle swarm optimization (SA-PSO) method, resulting in a more realistic computational model. Subsequently, a random crowd load model was established by combining the social force model (SFM) and the pedestrian load model, and a random crowd-floor mutual coupling calculation model was established based on the improved pedestrian biomechanical model. In addition, the mode shape functions of the floor with semirigid boundary conditions were obtained by extracting the optimized mode shape vector of the floor and using cubic spline interpolation. The dynamic response of the floor was computed using the modal analysis method, and the accuracy of the suggested method and model was verified by experiment. Furthermore, the effect on the vibration serviceability of the floor was analyzed under crowd walks randomly on the floor with different boundary conditions both before and after optimization. This study revealed: (1) achieving a computational model consistent with real floors requires optimization of relevant parameters and boundary conditions, reducing the error in floor frequency from 39.48% to 5.44% compared to measured results. (2) The human-induced vibration serviceability for existing floors may be misjudged by using traditional boundary conditions. The mean value of peak acceleration of floor with semirigid boundary conditions increased by 35.92%, with a 42% increase in the probability of serviceability problems compared to the SSCC boundary. (3) High-frequency floors also experience human-induced vibration serviceability issues. For a floor with a fundamental frequency of 10.3540 Hz, simulation and experimental results during five-person random walks indicate that peak acceleration at the middle position of the floor exceeds serviceability limits. [ABSTRACT FROM AUTHOR]

Porous materials have been extensively used in electronic communications, aerospace, bio-medicine and petrochemical, etc. due to their attractive attributes such as low relative density, thermal and acoustical insulation and good permeability. Ultrashort laser pulses have a series of unique advantages including high energy density, ultrashort interaction time and high accuracy, which are widely used in the fields of precision machining and microelectronic manufacture. For porous materials heated by an ultrashort laser pulse, revealing the interplay between deformation field and temperature field is crucial to guide their engineering application and optimization design. The present work devotes to investigating the transient response of a porous half-space heated by a non-Gaussian laser beam on its boundary surface based on the newly established linear thermoelastic theory with strain and thermal relaxations. The coupled governing equations are formulated and solved through the Laplace transform and its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress as well as volume fraction field are obtained and illustrated graphically. In calculation, the effects of the thermal relaxation factor, the strain relaxation factor on the temperature field, volume fraction field, displacement field as well as stress field are examined and discussed in detail. [ABSTRACT FROM AUTHOR]

As a main source of energy dissipation, thermoelastic damping (TED) cannot be ignored in designing resonators with high-quality factor. However, due to the size-dependent effect and the thermal relaxation, the TED models formulated in the classical theory are no longer able to accurately estimate the energy dissipation in the micro-/nano-resonators. To fill theses gaps, the present work aims at developing a new TED model for micro-plate resonators based on the modified couple stress theory incorporating memory-dependent derivative heat conduction model. The corresponding governing equations are derived, and the analytical solution for the TED is obtained. In order to discover the variation law of TED of micro-plate resonators, the numerical results corresponding to different materials and different theories are illustrated and compared. In calculation, the effects of the material parameters, the boundary conditions, the length scale parameters and the length on the peak value as well as the critical thickness of TED are further studied. It is expected that this novel model may provide a theoretical basis for designing high-performance micro-plate resonators under complex working conditions. [ABSTRACT FROM AUTHOR]

More realistic results of the random crowd-structural interaction dynamic response calculations are crucial for structural vibration analysis and control. And ignoring interactions is considered a conservative approach. This paper analyzes the effect of obstacles and semi-rigid boundary conditions on the random crowd-structure interaction vibration of the floor. The social force model is used to simulate crowd walking randomly in the room, and simulation results are matched with the dynamic calculation of the floor, thus establishing the time-varying dynamic calculation model of crowd-structure interaction. The differential quadrature method and mode analysis method are used to solve the dynamic equations. In addition, the effect of crowd random walking in an environment with obstacles on the time-varying parameters and dynamic response of the floor is discussed. The results show: (a) With the random walking of pedestrians, the floor fundamental frequency first decreases and then increases compared with the no-load, while the change of damping ratio is the opposite. Furthermore, the variation of floor fundamental frequency and damping ratio is greater in the empty classroom (without obstacles) than in the discussion room layout (with obstacles) due to the obstacles. (b) Analyzing the variation of the acceleration response of the floor under the two layouts, it can be found that the installation of obstacles can improve the human-induced vibration of the floor. (c) The vibration problem of the floor can be effectively improved by changing the stiffness ratio in semi-rigid constraint, which provides another idea for the vibration control of the floor. [ABSTRACT FROM AUTHOR]

The applicability of the Green–Naghdi (GN-III) thermoelasticity is increasingly questionable because the theory predicts that heat transfers with an infinite speed. To address this deficiency, the three-phase-lag (TPL) thermoelasticity was developed by introducing the lagging times into the GN-III thermoelasticity. On another front, the small-scale effect on elastic deformation cannot be ignored with the miniaturization of structures or devices. Meanwhile, the memory-dependent feature of heat transfer process in the case of ultrafast heating cannot be described by the integer-order heat conduction models due to the inherent local limited definition. To capture the small-scale effect and the memory-dependent effect of the microstructures, as a first attempt, the present work focuses on developing a TPL thermoelastic model by considering the memory-dependent derivative (MDD) heat conduction model and Eringen's nonlocal model. Then, the refined model is used to investigate the transient characteristics of a spherical microshell induced by thermal and mechanical loadings. The governing equations containing the modified parameters are derived and then solved by Laplace transform method. Some parametric results are demonstrated to display the effects of the time-delay factor, the kernel function, and the nonlocal parameter on the considered physical quantities. [ABSTRACT FROM AUTHOR]

Compared with the fractional order generalized themoelastic theory, the generalized thermoelastic theory based on the memory-dependent derivative has following significant advantages: First, the generalized thermoelastic theory with memory-dependent derivative has more specific physical meanings and can excellently describe that the present state of a system is dependent on its past states; Second, the memory-dependent derivative is based on the integer order calculus, which is more convenient to operate than fractional order model; Particularly, for different kernel functions, the time-dealy factor has different choice to adapt to different specific problems, which makes it greatly possible to describe the real thermoelastic response of medium. In present work, the transient response of an infinite rotating hollow cylindrical conductor with variable material properties subjected to a thermal shock at its inner surface is investigated based on the generalized thermoelastic theory with memory-dependent derivative. The hollow cylinder is placed in an external magnetic field with constant intensity, whose outer surface is traction free. The governing equations are formulated and then solved by using Laplace transform and its numerical inversion. The distributions of the dimensionless temperature, displacement, induced electric field, induced magnetic field, hoop stress as well as radial stress in the cylinder are obtained and illustrated graphically. The obtained results show that the kernel function, the time-delay factor and the temperature-dependent material properties influence the distributions of the considered variables more or less, while, the angular velocity significantly influence the variations of the dimensionless displacement, hoop stress and radial stress. [ABSTRACT FROM AUTHOR]

In order to obtain the transient thermoelastic diffusion responses of porous materials heated by the ultrashort pulse laser, the focus of this work is to establish a generalized thermoelastic diffusion theory considering strain, thermal and diffusion relaxation effect within the thermodynamic framework. Firstly, we derive the governing equations of the linear generalized thermoelastic diffusion theory of porous media in the context of the thermodynamic laws. Secondly, the copper material with voids occupying a half-space heated by the ultrashort pulse laser is investigated based on the built theory. The bounding plane is assumed to be traction free and impacted by a non-Gaussian laser beam. The exact solutions of the governing equations are obtained by Laplace transformation and the numerical inverse Laplace transformation. Finally, the effect of strain relaxation factor, thermal relaxation factor, fractional order parameter, and laser parameters on non-dimensional temperature, displacement, stress, volume fraction field, and chemical potential is studied and presented graphically. [ABSTRACT FROM AUTHOR]

The applicability of the generalized thermoelastic theories with integer-order derivative in solving anomalous or transient thermoelastic diffusion problems is questionable. Due to the feature of memory-dependence and heredity, the fractional-order derivative and the memory-dependent derivative are introduced to modify the generalized thermoelastic theories for extending their applicability. To demonstrate the features of such theories, the thermoelastic-diffusive dynamic response of an infinite elastic medium containing a spherical cavity with variable material properties is investigated in three different generalized theories with memory-dependent effect, which are incorporated in a unified form. Of them, two are based on fractional-order derivative and the other one is based on the memory-dependent derivative. The corresponding governing equations are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress, concentration and chemical potential under the three theories are obtained and illustrated graphically for comparing with those obtained from one of the integer-order theories. The effects of the fractional-order parameter, the time-delay factor, the variable thermal conductivity and diffusivity on the variations of the considered variables are considered and discussed in detail. [ABSTRACT FROM AUTHOR]

Porous materials have been widely used in aerospace, electronic communication, petrochemical and bio-medicine, etc. due to their attractive attributes such as low relative density, thermal and acoustical insulation and good permeability. For porous materials suffering high temperature gradient or ultrafast heating, etc., it is crucial to reveal the behaviors of the thermal-induced stress and deformation within them for guiding their potential applications and optimizations. In present work, the thermoelastic dynamic behaviors of a porous half-space subjected to a ramp-type heating is investigated based on the theory for thermoelastic porous materials and the three-phase-lag heat conduction model. The governing equations of the problem are formulated, and then, solved by using Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, stress and volume fraction within the half-space are obtained and illustrated graphically. In calculation, the effects of time, ramp-heating time factor and thermal time-delay factors on the considered physical quantities are examined and discussed in detail. Comparisons of the variations of the considered quantities under three different theories are carried out and presented. [ABSTRACT FROM AUTHOR]

With the rapid development of ultrafast heating technologies and its application in the micro-machining of micro/nano-electromechanical devices, where the nonlocal effects on elastic deformation and heat/mass transfer will increase and classical/generalized theory of thermoelastic diffusion coupling does not hold any more. In this work, a nonlocal theory of thermoelastic diffusive materials is developed, and the spatial nonlocal effects of heat and mass transport are both considered for the first time. With the aid of thermodynamic principles, the constitutive relations involving size-dependent characteristic lengths are derived. In the aspect of the application, the proposed theoretical model is further used to investigate the dynamic thermo-elasto-diffusive responses of a one-dimensional semi-infinite medium with one end subjected to time-dependent shock loads, and the semi-analytical techniques based on Laplace transform methods are applied to obtain the transient solutions. The effects of nonlocal parameters on structural dynamic thermo-elasto-diffusive responses are also evaluated and discussed to be expected to provide new insights on the thermoelastic diffusion coupling at the micro/nanoscale. [ABSTRACT FROM AUTHOR]

The present work devotes to investigating the transient responses of a half-space with variable thermal material properties based on the generalized thermoelastic theory with memory-dependent derivative. The bounding surface is assumed to be traction free and heated by a non-Gaussian laser beam. The material characteristic parameters are assumed as the linear function of temperature. The coupled governing equations containing thermal time-delay factor and kernel function, which can be chosen to adapt to specific problems, are formulated and solved by the Laplace and Kirchhoff transformations. Numerical results of the non-dimensional temperature, displacement as well as stress under different time, variable thermal conductivity, thermal time-delay factor and kernel function are obtained and illustrated graphically. It is hoped that the obtained results would be helpful in designing the temperature-dependent structures heated by a non-Gaussian laser beam in engineering. [ABSTRACT FROM AUTHOR]

Elastoplastic nonlinear bending behaviors of ceramic–metal composite functionally graded material (FGM) beams are investigated using the symplectic method in Hamilton system with the classical beam theory. The mechanical properties of two-phase materials are assumed to be power function of the thickness, and the elastoplastic material properties of the FGM beams are given by the linear rule of mixtures. The bilinear hardening elastoplastic constitutive equations are established based on the Tamura–Tomota–Ozawa hybrid reinforcement model. And the von-Mises yield condition is introduced to judge whether the beams have entered the plastic deformation. The canonical equations are solved by the symplectic method, and the loads and deflections are transformed into the symplectic eigenvalues and symplectic eigensolutions in symplectic space and obtained by analytical solutions. Examples of bending behaviors varying with load, deflection, slenderness ratio and power law index are presented. The obtained results reveal that the zones of the elastic bending and the elastoplastic bending as well as the peak values of the deflections vary with material and geometric properties. [ABSTRACT FROM AUTHOR]

Multi-cell storage devices (e.g. lithium-ion batteries (LIBs)) stand as one of the most important components which are widely used in battery energy storage technology for renewable energy power system, hybrid electric vehicles and portable electronic devices due to its high energy density and low manufacturing cost. In recent years, there has been an explosion of developing new and multifunctional nanomaterials with particular interest to electrode nanomaterials (nano-MnO2, nano-LiMn2O4, etc.). In such case, size-dependent mechanical-diffusion responses analysis of multilayered composite nanostructure under non-uniform concentration in-service environment will become significantly important. To address the problem, a multilayered composite nanoplates account for diffusion impedance and elastic wave impedance at the interface is considered in this research. Governing equations involving with size-dependent characteristic lengths and material constant ratio of each two adjacent layers are formulated, and then, a semi-analytical approach via the Laplace transformation is applied. Then, the obtained solutions are applied to bilayered composite nanoplates, and the influences of size effects and material constants ratio on structural responses are emphatically discussed to provide guidelines on and new insights into the optimal design and management of mechanical responses and vibration control of nano-sized multi-cell storage devices under non-uniform concentration environment, especially for the nano-coating. [ABSTRACT FROM AUTHOR]

Based on the generalized thermoelasticity with memory-dependent derivative, the transient response of a half-space heated by a non-Gaussian laser beam on its boundary is investigated. The coupled governing equations containing thermal time-delay factor and thermal kernel function, which can be chosen to adapt to specific problems, are formulated and solved by the Laplace transform technique and its numerical inversion. For the functionally graded half-space, its material properties are assumed to exponentially vary with material coordinate. In calculation, the non-dimensional temperature, displacement as well as stress under different thermal time-delay factor, thermal kernel function and functionally graded parameter are obtained and illustrated graphically. The results show that: with the decrease of thermal time-delay factor or the increase of exponent n of thermal kernel function, the peak value of the non-dimensional temperature, displacement and the absolute value of peak value of stress increase; negative temperature value, positive displacement and stress values will appear when functionally graded parameter is less than zero. It is hoped that the obtained results would be helpful in designing the functionally graded materials heated by a non-Gaussian laser beam in engineering. [ABSTRACT FROM AUTHOR]

Due to the advantages of high-power density, short duration, and high machining accuracy, ultrashort laser pulses are widely used in the fields of ultra-precision machining and microelectronic manufacture. In the manuscript, the L-S generalized thermoelastic diffusion theory considering the memory-dependent effect and spatial nonlocal effect is established and the thermoelastic diffusion responses of a semi-infinite thin plate subjected to a non-Gaussian laser pulse and a chemical shock on its boundary are studied. The Laplace integral transformation and its numerical inversion are used to solve the problem. The variation of the temperature, chemical potential, displacement, stress, and concentration with different nonlocal parameters, time delay factors, and kernel functions are obtained. The results show that heat conduction has a significant effect on mass transfer, while mass transfer has little effect on heat conduction; nonlocal parameter has a significant influence on displacement and stress, but little effect on temperature, chemical potential, and concentration. The establishment of this theory and the solution of the corresponding problem are aimed at reasonably predicting the transient responses of heat conduction and mass transfer under the coupling effects of mechanics, heat, and diffusion. [ABSTRACT FROM AUTHOR]

The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative. Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously. It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The influences of the material characteristic parameters at the interface on the structural responses are emphatically discussed, and the non-dimensional temperature, chemical potential, displacement, stress as well as concentration at different values of time delay factors and kernel functions are obtained and illustrated graphically. The results show that: the changes of the time delay factors, kernel functions, and material characteristic parameters have the varying degrees of influences on the considered variables. Based on the above conclusions, the sandwich structure working under the thermoelastic diffusion coupling condition can be designed reasonably. [ABSTRACT FROM AUTHOR]

In the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source is investigated. The corresponding governing equations are formulated and solved by means of Laplace transform and its numerical inversion. In simulation, the effects of the time-delay factor, the kernel function and the nonlocal parameter on the distributions of the non-dimensional temperature, displacement and stress are examined, respectively, and illustrated graphically. The results show that: the time-delay factor and the kernel function significantly affect the peak values of the considered variables; the nonlocal parameter barely influences the distributions of the non-dimensional temperature, slightly influences the peak values of the non-dimensional displacement, while remarkably influences the peak values of the non-dimensional stress. [ABSTRACT FROM AUTHOR]

In present work, the transient responses of a hollow cylindrical conductor based on the generalized thermoelastic theory with memory-dependent derivative are investigated. The conductor with temperature-dependent mechanical properties is subjected to a thermal shock on its internal surface. The hollow cylindrical conductor is placed in a magnetic field along the axial direction of the cylinder. The effects of memory-dependent derivative and temperature-dependent properties influenced by the variable material property factors on the heat conduction and structural responses are emphatically discussed. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The distributions of the non-dimensional induced electric field, induced magnetic field, hoop stress, radial stress, temperature and displacement at different values of time delay factors, kernel functions and variable material property factors are obtained and illustrated graphically. Finally, some conclusions are summed up, based upon which guidelines may be provided in the design of a hollow cylindrical conductor working in a thermo-mechanical coupling environment. [ABSTRACT FROM AUTHOR]

Dielectric elastomers are capable of large deformation subject to an electric voltage and are promising for use as actuators, sensors, and generators. Because of large deformation, nonlinear equations of states, and diverse modes of failure, modeling the process of electromechanical transduction has been challenging. This paper studies a membrane of a dielectric elastomer deformed into an out-of-plane axisymmetric shape, a configuration used in a family of commercial devices known as the universal muscle actuators. The kinematics of deformation and charging, together with thermodynamics, leads to equations that govern the state of equilibrium. Numerical results indicate that the field in the membrane can be very inhomogeneous, and that the membrane is susceptible to several modes of failure, including electrical breakdown, loss of tension, and rupture by stretch. Care is needed in the design to balance the requirements of averting various modes of failure while using the material efficiently. [ABSTRACT FROM AUTHOR]

AbstractFunctionally graded materials (FGMs) stand as one of the most representative composite materials due to the superior thermal resistance in non-isothermal environment. On another front, the applicability of integer-order heat conduction models is increasingly questionable because the heat transfer shares the history-dependent property at time microscale. It is noted that the small-scale effect of elastic deformation has become significant due to the development of micro-devices. To capture the small-scale effect of elastic deformation and the memory-dependent effect of heat conduction in the FGM microstructures, as a first attempt, the present study focuses on developing a thermoelastic model by incorporating the fractional-order dual-phase-lag (FODPL) heat conduction model and the Eringen’s nonlocal model. Moreover, the extension of the Caputo definition, i.e., the Tempered-Caputo (TC) definition of fractional derivative ruling out singular kernel is adopted to depict the memory-dependent effect of the heat conduction. Then, the modified model is used to investigating the dynamic response of a FGM spherical microshell subjected to a sinusoidal thermal-mechanical loading. The corresponding governing equations are formulated and then solved by Laplace transform techniques. Some parametric results are demonstrated to display the influences of the fractional-order parameter, the nonlocal parameter and the power-law index on the considered physical quantities. [ABSTRACT FROM AUTHOR]

AbstractThis work aims to study the nonlinear transient coupled thermo-electromechanical dynamic responses of the piezoelectric structure with the high-order temperature-dependent material properties. The multi-field coupling nonlinear model is established based on the non-Fourier thermoelasticity theories by introducing the function of high-order temperature dependency of the arbitrary material property. The virtual work principle and the nonlinear finite element approach are proposed to investigate the two-dimensional case of the orthotropic rectangular piezoelectric plate of the crystal class mm2 subjected to the zonal transient heating loads. The influences of the high-order temperature-dependent material parameters on the structural responses and wave propagations are discussed. [ABSTRACT FROM AUTHOR]

With the rapid development and applications of micro/nano electromechanical systems in engineering fields, piezoelectric materials have been widely used in these systems due to their excellent physical and mechanical properties. Generally, these systems work in complex thermoelastic environments, to depict the thermal-electro-mechanical behaviors of piezoelectric material structures at microscale, the existing theories need to be developed due to the arising size-dependent effect, thermal relaxation effect and flexoelectric effect etc. To this end, the present work intends to generalize the size-dependent theories by considering the thermal-electro-mechanical coupling behaviors in piezoelectric material structures at microscale. Based on the nonlocal strain gradient theory and the generalized heat conduction model, a new model is established and the corresponding constitutive equations and the governing equations of equilibrium are derived. To illustrate the application of this new model, a piezoelectric micro-beam with flexoelectricity is considered and the closed form solutions of bending deflection and the free vibration response are obtained in terms of the boundary conditions. Based on the numerical results, the size-dependent effect, the piezo-flexoelectric effect and the thermal-lagging effect on the bending and vibration responses of the microbeam are examined and illustrated graphically. This work may be potentially helpful for the efficient, optimized and adaptive designs of the NEMS/MEMS devices. [ABSTRACT FROM AUTHOR]

Nowadays, the nanosandwich structure stands as one of the most promising candidates for nanodevices and nanocomposites (e.g., nanogenerator, nano-energy harvester) due to its superior mechanical properties. The size-dependent response analysis of nanosandwich structure under extreme in-service environment is of great importance for its fabrication and exploitation. This motivates us to study the transient responses of nanosandwich structure subjected to the symmetrical transient thermal and chemical potential shock loads, which are both imposed on its upper and lower bounding surfaces. It is further assumed that thermal contact resistance and diffusional contact impedance at the interface of each two adjacent layers are zero with ideal adhesion. For each isotropic homogeneous elastic layer, the governing equations are formulated in the context of size-dependent generalized thermoelastic diffusion theory and then are solved by using Laplace transformation techniques. The effects of elastic nonlocal parameter, fractional order parameters as well as material characteristic parameters on structural transient responses are also analyzed and discussed. The present study not only provides a comprehensive understanding of the size-dependent thermoelastic diffusion coupling of nanosandwich structure, but also offers basic guidelines for optimal design. [ABSTRACT FROM AUTHOR]

In the context of a memory-dependent generalized thermoelasticity, the thermal-induced transient response in an infinite elastic body containing a spherical shell is investigated. A thermal shock is applied on the inner surface of the spherical shell. The infinite body and the spherical shell are assumed to be isotropic but two dissimilar materials. By using an analytical technique based on the Laplace transform along with its numerical inversion, the governing equations of the problem are solved and the non-dimensional physical quantities in the two materials, i.e., temperature, displacement and stress, are obtained and illustrated graphically respectively. In simulation, the accuracy of memory-dependent derivative (MDD) is verified by degrading the present model into L-S model to compare the results obtained from the cases with interfacial thermal resistance and without interfacial thermal resistance. In addition, the effects of the different kernel functions as well as the ratios of the two materials, including the ratios of the density, the thermal-conductivity and the time-delay, on the distributions of the considered variables are obtained and demonstrated graphically respectively. [ABSTRACT FROM AUTHOR]

The dynamic response of a one-dimensional thermo-piezoelectric problem with variable material properties is investigated in the context of fractional order theory of thermoelasticity. The system of governing equations for the thermo-piezoelectric problem is formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered non-dimensional displacement, temperature, and stress are obtained and illustrated graphically. The effects of fractional order parameter and temperature-dependent properties on the considered quantities are investigated and the results show that they have significant influence on the variations of the considered quantities. [ABSTRACT FROM AUTHOR]

Based on the generalized thermoelastic diffusion theory with memory-dependent derivative in both the generalized heat conduction law and the generalized diffusion law, the transient response is investigated of a half-space subjected to a thermal shock and a chemical potential shock on its bounding surface. The coupled governing equations containing time-delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The non-dimensional temperature, chemical potential, displacement, stress, as well as concentration at different values of time, time-delay factors, and kernel functions are obtained and illustrated graphically. The results show that: all the considered variables have obvious changes with the passage of time; the thermal time-delay and kernel functions hardly influence the distributions of the non-dimensional chemical potential, modestly influence the distributions of the non-dimensional concentration, while appreciably influence the distributions of the non-dimensional temperature, displacement, and stress; the diffusion time-delay and kernel functions barely affect the distributions of the non-dimensional temperature, slightly affect the distributions of the non-dimensional concentration, while remarkably affect the distributions of the non-dimensional chemical potential, displacement and stress. [ABSTRACT FROM AUTHOR]

Nano-batteries have been widely used in electric vehicles, new energy, and aerospace engineering since their high energy density, low manufacturing cost, and long cycle life. In recent years, there have been many papers that contributed to investigate the diffusion-mechanical coupling problems under non-uniform molar concentration environments (e.g., rapid charging, etc.). Nevertheless, the memory dependence of strain relaxation and mass transfer has not been considered yet. This paper aims to construct a unified fractional-order non-Fick mechanical-diffusion coupling model by introducing the fractional derivatives of the Caputo (C), Caputo–Fabrizio (CF), Atangana–Baleanu (AB), and Tempered-Caputo (TC) types. The proposed theoretical model is applied to investigate structural transient dynamic responses of multilayered composite laminates with imperfect interfacial conditions by Laplace transformation approach. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on the wave propagations and dynamic mechanical-diffusion responses are evaluated and discussed in detail. [ABSTRACT FROM AUTHOR]

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer (DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices. [ABSTRACT FROM AUTHOR]

The present work is devoted to establishing the ultrashort pulse laser ablation generalized thermoelastic model with spatio-temporal nonlocal effect and investigating the transient responses of the process of silicon ablated by the picosecond pulse laser. The research is divided into three cases. 1) The solid silicon before the target surface melting is studied, and the transient responses of the final state of this case are taken as the initial conditions of the Case Two. 2) The liquid silicon after the target surface melting is researched, and the heat flux taken away by vaporization is considered in the boundary condition. 3) The solid silicon after the target surface melting is discussed, and the moving solid-liquid interface is regarded as the coordinate origin. The coupled governing equations containing spatial nonlocal parameter, time delay factor, and kernel function are established and solved by the Laplace transform together with its numerical inversion. The melting time and depth of target are emphatically discussed. The temperature, displacement and stress with different laser intensity, spatial nonlocal parameter, time delay factor, kernel function as well as time are obtained and illustrated graphically. [ABSTRACT FROM AUTHOR]

The transient thermo-piezoelectric response of a functionally graded piezoelectric rod subjected to a moving heat source is investigated in the context of fractional order theory of thermoelasticity proposed by Sherief. The material properties of the functionally graded piezoelectric rod are assumed to vary exponentially along the length, except for the thermal relaxation time and the specific heat, which are taken to be constant. To solve the governing equations of the problem, Laplace transform is applied, eliminating the time effect; the analytical solutions of the displacement, stress, temperature, and electric field in Laplace domain are obtained. Subsequently, the solutions of the considered variables in time domain are obtained by numerical Laplace inversion and illustrated graphically. In calculation, the effect of the fractional order parameter on the variations of the considered variables is presented. [ABSTRACT FROM PUBLISHER]

The dynamic response of a piezoelectric-thermoelastic rod made of piezoelectric ceramics (PZT-4) subjected to a moving heat source is dealt with in the context of the fractional order theory of thermoelasticity. The piezoelectric-thermoelastic governing equations for the problem are formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered nondimensional temperature, displacement, stress, and electric potential are obtained and illustrated graphically. The effects of fractional order parameter and the velocity of heat source on the variations of the considered variables are investigated, and the results show that they have significant influence on the variations of the considered variables. The present investigation could be helpful for better understanding the multi-field coupling effect of mechanical, electric, and thermal fields in real piezoelectric ceramics structures, and provide some guidelines in the optimal design of actuators or sensors made of piezoelectric ceramics serving in a thermoelastic environment. [ABSTRACT FROM PUBLISHER]

Abstract In recent years, the application of porous materials in practical engineering has become increasingly common. Under extreme thermal conditions, how to accurately describe the heat conduction and structural response of porous materials is a key issue in the structural safety and functional design of porous materials. Among them, it is particularly important to consider the size-dependent and memory-dependent effects for small-sized structures or microdevices of porous materials. To address these issues of porous structures and to guide their applications as well as optimization, this paper first investigates the thermoelastic transient response of porous microplates subjected to thermal and stress shocks at the left boundary based on the Atangana-Baleanu (AB) fractional-order generalized thermoelastic theory by considering nonlocal effects and fractional-order strain, which is combined with the thermoelasticity theory of porous materials and the dual-phase-lag (DPL) heat conduction model. The governing equations are then established and solved using the Laplace transform and its numerical inversion. Finally, the effects of newly defined fractional order parameters, nonlocal parameters and the initial magnitude of the mechanical shock on the dimensionless temperature, volume fraction field, displacement and stress distribution are discussed and displayed graphically. [ABSTRACT FROM AUTHOR]

In order to capture the memory-dependent effect and size-dependent effect, present work aims to develop a novel thermo-viscoelastic nonlocal model in micro-scale for the first time to include the simultaneous effects of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function. Then, the theory is applied to studying the dynamic response of a polymer microbeam heated by a ramp-type heating. In calculation, the influences of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function on the variations of the considered variables are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

The dynamic response of a two-dimensional generalized thermoelastic diffusion problem for a half-space is investigated in the context of the generalized thermoelastic diffusion theory. The half-space is subjected to a thermal shock and a chemical potential shock on its bounding surface. The governing equations of this problem are formulated, and due to the complexity of the equations, a numerical method, i.e., hybrid Laplace transform-finite element method, is used to solve them. The non-dimensional temperature, displacement and chemical potential are obtained and illustrated graphically. The results show that the non-zero values of all the considered variables are only in a bounded region and vanish identically beyond this region, and the propagating speed of diffusive wave is larger than that of thermoelastic wave. [ABSTRACT FROM AUTHOR]

A two-dimensional generalized electromagnetothermoelastic problem for a half-space with diffusion is investigated in the present work. The problem is formulated in the context of the generalized thermoelastic diffusion theory. The half-space is initially placed in an external magnetic field with constant intensity, and its bounding surface in contact with a permeating substance is taken to be traction free and subjected to a time-dependent thermal load. The chemical potential is also assumed to be known function of time on the bounding surface. The half-space deforms because of the thermal load, and due to the application of magnetic field, there results in an induced magnetic field and an induced electric field in the half-space. The system of Maxwell's equations is given and the generalized electromagnetothermoelastic diffusive coupled governing equations are established. To solve the formulated equations, normal mode analysis is adopted and the exact expressions for the non-dimensional temperature, displacement, stress, induced magnetic field, induced electric field, and chemical potential and concentration are obtained and represented graphically. [ABSTRACT FROM AUTHOR]

Nano sandwich-like storage structure or device is commonly designed as diaphragm to extend nano-battery working life, or fabricated as nanocomposite anode materials to maximumly improve electrochemical performance in nano-battery systems. This work aims to investigate size-dependent dynamic mechanical-diffusion responses of multi-layered laminated sandwich-like nanocomposites subjected to shock loadings of molar concentration in the context of nonlocal diffusion-elasticity model by a semi-analytical technique via Laplace transformation. The results reveal that the diffusion isolation will be maximally improved and lager harmful chemical stresses can be reduced to some extent for proper materials nonlocal parameters and constants ratios of selected. [ABSTRACT FROM AUTHOR]

The relaxation process of viscoelastic materials has the memory-dependent effect, while integer-order thermo-viscoelastic models may be challenged to predict precise thermal–mechanical behaviors in solving transient problems of viscoelastic materials in a heat transfer environment. It is found that the fractional-order viscoelastic models fit well with the experimental data from creep and relaxation tests. Additionally, the size-dependent effect on elastic deformation is becoming an issue of great importance recently due to the development of small-scale devices. To capture the memory-dependent and size-dependent effects, the present work aims to formulate a modified fractional-order thermo-viscoelastic model at small-scale for the first time by simultaneously incorporating the effects of the unified definition of the fractional-order parameter, the unified definition of the fractional-order strain parameter and the nonlocal parameter based on the generalized thermo-viscoelastic theory. Then the dynamic response of a viscoelastic microplate under a thermal shock is studied by using the modified fractional-order thermo-viscoelastic model. The corresponding governing equations are formulated and solved by the Laplace transform and its numerical inversion. In conclusion, the influences of the fractional-order parameters, the fractional-order strain parameters and the nonlocal parameters on the variations of the considered quantities are presented and discussed in detail. The obtained results show that these parameters significantly influence the variations of all the considered quantities. [ABSTRACT FROM AUTHOR]

Abstract: The generalized thermoelastic theory with thermal relaxation, in the context of Lord and Shulman theory, is used to investigate the magneto-thermoelastic problem of a thin slim strip placed in a magnetic field and subjected to a moving plane of heat source. The generalized magneto-thermoelastic coupled governing equations are formulated. By means of the Laplace transform and numerical Laplace inversion, the governing equations are solved. Numerical calculations for the considered variables are performed and the obtained results are presented graphically. The effects of moving heat source speed and applied magnetic field on temperature, stress and displacement are studied. It is found from the graphs that the temperature, thermally induced displacement and stress in the strip are found to decrease at large heat source speed, and the magnetic field significantly influences the variations of non-dimensional displacement and stress. However, it has no effect on the non-dimensional temperature. [Copyright &y& Elsevier]

• TED is first established in nonlocal strain gradient theory with dual-phase-lag model. • The equations with scale effects on TED are solved by complex frequency method. • The effects of scale parameters and material properties on TED are examined. • Both stiffness hardening and softening effects are captured. • The present method is useful to evaluate TED in nanomechanical resonators. Thermoelastic damping (TED), as a main source of intrinsic energy dissipation, is crucial to the design of the micro/nano-devices and -systems with higher quality factor (Q -factor). However, the classical analysis model of TED fails in micro/nano-scale due to the influence of small-scale effect. The present article focuses on investigating the influence of scale effect on the TED of micro-beam resonators by considering stress nonlocal and higher-order strain gradient effects. Firstly, the governing differential equations are formulated by employing the nonlocal strain gradient theory (NSG) in conjunction with the dual-phase-lag (DPL) heat conduction model. According to the assumption of vibration mode and the boundary conditions, the size-dependent Q -factor expression of TED is derived by the complex frequency method. Finally, the influences of various parameters on the TED of micro-beam resonators, such as nonlocal parameter, length scale coefficient, slenderness ratio and material type, are discussed in detail. And then, the analysis results are compared with the TED of classical thermal-mechanical model. This article provides a novel theoretical analysis model of the TED in micro/nano-meter scale field, which has practical significance in the design of high-efficiency devices and systems. [ABSTRACT FROM AUTHOR]

Abstract: Based on the Lord and Shulman generalized thermo-elastic theory with one relaxation time, the dynamic thermal and elastic responses of a piezoelectric rod fixed at both ends and subjected to a moving heat source are investigated. The generalized piezoelectric–thermoelastic coupled governing equations for piezoelectric rod are formulated. By means of Laplace transformation and numerical Laplace inversion the governing equations are solved. Numerical calculation for stress, displacement and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. [Copyright &y& Elsevier]

A two-dimensional coupled problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a time-dependent heat is studied in this paper. The problem is in the context of the Green and Lindsay's generalized thermoelasticity theory with two relaxation times. There acts an initial magnetic field parallel to the plane boundary of the half-space. The medium deforms because of heat, and due to the application of the magnetic field, there results an induced magnetic field and an induced electric field in the medium. The Maxwell's equations are formulated and the electromagneto-thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. [ABSTRACT FROM AUTHOR]

Abstract: The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to study the electromagneto-thermoelastic interactions in an infinitely long perfectly conducting solid cylinder subjected to a thermal shock on its surface when the cylinder and its adjoining vacuum is subjected to a uniform axial magnetic field. The cylinder deforms because of thermal shock, and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the cylinder. The Maxwell''s equations are formulated and the generalized electromagneto-thermoelastic coupled governing equations are established. By means of the Laplace transform and numerical Laplace inversion the problem is solved. The distributions of the considered temperature, stress, displacement, induced magnetic and electric field are represented graphically. From the distributions, it can be found the electromagnetic-thermoelastic coupled effects and the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier''s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. [Copyright &y& Elsevier]

• A new rate-dependent constitutive model of thermo-electromechanical coupling is developed within extended thermodynamics. • Structural responses to multilayered laminated piezoelectric composites with imperfect interfacial conditions are investigated. • Strain and electric rates efficiently eliminate abrupt jumps of structural responses at elastic and thermal wave fronts. • Rationally adopting parameters ratios remarkably lift stress isolation and electric energy harvesting. Thermo-electromechanical coupling analysis at micro/nano-seconds appears to be particularly important, where strain and electric relaxation effects will increase significantly in such case. So far, although temperature-rate-dependent theory of piezoelectric thermoelasticity has been historically proposed, it may be no longer hold anymore as relaxation effects both in electrical and strain fields have not been fully considered yet. This work mainly contributes to constitutive modeling of a novel rate-dependent piezoelectric thermoelasticity by considering time-derivatives terms of the elastic strain, relative temperature, and electric intensity associated with related relaxation time parameters. Constitutive and field equations are strictly derived via extended thermodynamics. Newly developed theoretical model is applied to analyze structural thermo-electromechanical responses of multilayered laminated piezoelectric smart composites accounting for contact imperfection and material parameters via a semi-analytical integrated transformation technique. Dimensionless results reveal that the properly selecting thermal/stain/electric relaxation time parameter or considering non-idealized boundary conditions at interface of multilayered laminated piezoelectric smart composites will maximally enhance the electric energy harvesting, realize the displacement control, and improve the harmful stress isolation. [ABSTRACT FROM AUTHOR]

For nano/micro-scale structures, the classical continuum mechanics can't properly depict the size-dependent effect arising in them anymore. In addition, Fourier's law is limited in describing the heat transfer process in nano/microstructures due to its nature of predicting infinite heat speed. To amend such defects, the non-classical continuum mechanics based on the nonlocal elasticity theory and the modified couple stress theory incorporating the non-Fourier heat transfer model with memory-dependent effect is formulated to characterize the thermoelastic behaviors in micro/nano-scale system in the present work. Then, the model is used to study the dynamic response of an Euler-Bernoulli nanobeam subjected to a ramp-type heating. The corresponding governing equations are derived and then solved by Laplace transform method and its numerical inversion. The distributions of the non-dimensional transverse deflection, temperature and displacement are obtained and illustrated graphically. In calculation, the influences of the ramp heating time parameter, the material length parameter, the nonlocal parameter, the time-delay factor and the kernel functions on the considered physical quantities are examined and discussed in detail. [ABSTRACT FROM AUTHOR]

In recent years, the influence of size-dependent effect on elastic wave propagation in viscoelastic single-walled carbon nanotubes (SWCNTs) has been considerably investigated. Due to the excellent thermal conductivity of viscoelastic SWCNTs, it is very meaningful to study the influence of size-dependent effect on thermoelastic wave propagation properties in viscoelastic SWCNTs under thermal environment. Nevertheless, few theoretical investigations have been carried out to predict the thermoelastic wave propagation properties of viscoelastic SWCNTs in the existing literatures. To fill this gap, the present work aims to establish the thermoelastic coupling model for viscoelastic SWCNTs based on the Euler-Bernoulli beam theory by combining the nonlocal elasticity theory and the G-N theory, taking the surface effect into account. By assuming the wave type solutions, the dispersion relationship between frequency (or phase velocity) and wave number is determined. The influences of the nonlocal parameter, the surface effect and the damping coefficient on the thermoelastic wave dispersion relation of viscoelastic SWCNTs at two different diameters are examined and the thermoelastic wave propagation properties are presented graphically. • The wave propagation characteristics of viscoelastic single-walled carbon nanotubes in thermal enivornment are investigated. • The equation is solved by introducing the wave propagation general solution of deflection and temperature. • The thermoelastic coupling effect has a role in reducing magnitudes of the frequency and phase velocity for SWCNTs. • The work can provide some guidance for the design and optimization of micro/nano structures in thermal environment. [ABSTRACT FROM AUTHOR]

To accurately predict transient thermoelastic diffusion responses of the metallic solids in nanoscale heating condition, this work aims to establish a nonlocal dual-phase-lag Cattaneo-type thermoelastic diffusion theory by simultaneously consider the nonlocal effects of elastic deformation, heat and mass transport with the aid of Eringen’s nonlocal continuum mechanics. The proposed model is applied to investigate 1D transient dynamic response for copper-metallic layered structure by using eigenvalue approach. The influences of nonlocal characteristic lengths on the structural dynamic responses and wave propagations are evaluated and discussed. [ABSTRACT FROM AUTHOR]

Functionally graded (FG) laminated micro/nanostructures reinforced with graphene nanoplatelets (GPLs) stand as one of the most promising candidates for composite structures due to the excellent thermo-mechanical properties. Meanwhile, thermoelastic damping (TED) is one of the key factors to lower quality factor in micro/nanoresonators. Nevertheless, the classical TED models fail to explain the thermo-mechanical behavior considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present study aims to investigate TED analysis of FG laminated microplate resonators reinforced with GPLs in the frame of the modified strain gradient theory and the three-phase-lag heat conduction model. Four patterns of GPLs distribution including the UD, FG-O, FG-X and FG-A pattern distributions are taken into account, and the effective material properties of the plate-type nanocomposite are evaluated according to the Halpin–Tsai model. The energy equation and the motion equation based on the Kirchhoff microplate model are solved, and then, the closed-from analytical expression of TED is obtained by complex frequency technique. A detailed parametric study has been conducted to discuss the influence of the material length-scale parameter, the phase-lag parameters and the total weight fraction of GPLs on the TED. Results demonstrated that the energy dissipation of FG laminated microplate resonators reinforced with GPLs is determined by the size-dependent effect, the thermal lagging effect and the total weight fraction of GPLs. This results are helpful to the design of FG laminated microplate resonators reinforced with GPLs with high-performance for theoretical approach. [ABSTRACT FROM AUTHOR]

• A novel TED model is established. • Analytical expression of the TED model is obtained. • The TED model can reduce to the classical TED model. • A critical thickness is proposed. • Small scale significantly improves TED within the critical thickness. Thermoelastic damping (TED) is one of the main energy dissipation sources of high performance resonators at room temperature, however, the classical TED model fails at the nano-scale due to the influence of small scale effect. In this paper, a novel TED model is proposed to estimate the impact of both mechanical and thermal small scale effects on TED of nano-resonators. The surface elastic theory and the dual-phase-lag heat conduction model (DPL model) are first combined to establish the TED model. Analytical expression of the TED model is derived, which can reduce to the classical TED model. In numerical simulations, a critical thickness is proposed to identify the influence of small scale effect on TED. Small scale effect significantly improves TED of resonators within the critical thickness, which however can be neglected as the resonator thickness is greater than the critical thickness. Moreover, surface effect has stronger effect than non-Fourier heat conduction on improving TED of nano-resonators. Additionally, influences of the other key factors on TED are examined in detail. This paper provides a more reasonable theoretical approach to estimate TED in the design of high performance nano-resonators. [ABSTRACT FROM AUTHOR]

In this paper, to better reveal the surface effect and the screening effect as well as the nonlinear multi-field coupling characteristic of the multifunctional piezoelectric semiconductor (PS) nanodevice, and to further improve its working performance, a magneto-mechanical-thermo coupling theoretical model is theoretically established for the extensional analysis of a three-layered magneto-electro-semiconductor coupling laminated nanoplate with the surface effect. Next, by using the current theoretical model, some numerical analyses and discussion about the surface effect, the corresponding critical thickness of the nanoplate, and the distributions of the physical fields (including the electron concentration perturbation, the electric potential, the electric field, the average electric displacement, the effective polarization charge density, and the total charge density) under different initial state electron concentrations, as well as their active manipulation via some external magnetic field, pre-stress, and temperature stimuli, are performed. Utilizing the nonlinear multi-field coupling effect induced by inevitable external stimuli in the device operating environment, this paper not only provides theoretical support for understanding the size-dependent tuning/controlling of carrier transport as well as its screening effect, but also assists the design of a series of multiferroic PS nanodevices. [ABSTRACT FROM AUTHOR]