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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]

This article, published in the International Journal of Applied Mechanics, discusses a new theory of fractional-order rate-dependent piezoelectric thermoelasticity and its application in analyzing the structural transient response of smart piezoelectric composite laminates. The authors develop unified forms of fractional-order strain and heat conduction by adopting different types of fractional derivatives. They establish a fractional-order rate-dependent piezoelectric thermoelasticity theory and derive constitutive and governing equations using an extended thermodynamics framework. The theory is then applied to investigate the dynamic thermo-electromechanical responses of smart piezoelectric composite laminates with imperfect interfacial conditions. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on wave propagations and structural thermo-electromechanical responses are evaluated and discussed. [Extracted from the article]

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]

With the extensive applications of the micro/nano-electro-mechanical systems, a great deal of attention has been paid to explore the influences of the arising size-dependent effect and surface effect on their performance. Along with these effects, the nonlocal elasticity, strain gradient theory, and surface elasticity theory were successively proposed. Moreover, it is inevitable for MEMS/NEMS to work in a variable temperature environment, correspondingly, the thermal-induced stress or deformation becomes another issue that needs serious concern. Thermoelastic damping (TED), as a main energy dissipation source, is a major challenge in designing higher-quality factor resonators. However, considering the thermoelastic coupling effect, the aforementioned theories are not capable enough to depict the thermoelastic performance of micro/nano-resonators. To amend this deficiency, based on nonlocal strain gradient theory, a new model for assessing the TED of nanobeam resonators by incorporating the thermal relaxation effect and the surface effect is developed. The corresponding governing equations for the Euler–Bernoulli microbeam resonator model are formulated, and then, solved by means of a complex frequency method. The influences of the nonlocal parameter, strain gradient coefficients, aspect ratio, surface stress and surface elasticity on the TED are examined and discussed in detail. [ABSTRACT FROM AUTHOR]

With the rapid evolution of small‐scale devices, the effect of size dependence on elastic deformation becomes more and more obvious. Furthermore, the physical processes usually involve memory and inheritance for some anomalous diffusion that the constitutive relation does not obey the standard gradient rate. Owing to capturing the memory‐dependent effect and the size‐dependent effect, the existing thermoelastic diffusion theories cannot be applicable. To further refine the thermoelastic diffusion model for micro/nano structures, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional‐order dual‐phase‐lag (DPL) heat conduction model and fractional‐order diffusion model in this paper. In addition, the Tempered‐Caputo (TC) definition is an extension of the Caputo definition without the fractional derivative of the singular kernel, which is adopted for the first time to reflect the memory‐dependent effects of heat conduction and stress–strain relationship. Then, this new model is applied to investigating the transient response of an elastic microplate subjected to a sinusoidal thermal loading. The corresponding governing equations are formulated and solved by the Laplace transform method and its numerical inversion. In calculation, the influences of the fractional‐order parameter, the tempered parameter and the nonlocal parameter on the variations of the considered quantities are presented and discussed in detail. It is expected to provide new insights into thermoelastic diffusion behaviors of structures at the micro/nanoscale. [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]

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]

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]

With the great development of micro-electromechanical devices and wide application of subpicosecond/femtosecond ultrafast laser technology in micro-machining of micro-electromechanical devices, the investigations of interactions between thermodiffusion and deformation become significantly important. To accurate modeling the thermo-elasto-diffusive coupling, a new time fractional-order (i.e. memory-dependent derivative) based model of generalized thermoelastic diffusion for a perfect thermally and isotropic conducting medium which is assumed to have variable thermal conductivity and diffusivity is given in this work. This model is applied to investigate transient responses of a spherical shell subjected to instantaneous thermal and chemical shock loadings at external surface, whilst it is assumed that a permeating substance is in contact with the rigid surface at its internal surface. The solutions in the Laplace transform domain are obtained by using Kirchhoff and Laplace transform techniques and then the numerical inversion process based on fast Fourier transformation is carried out to derive the transient solutions in the time domain. Numerical computations for all the physical quantities considered are implemented and represented graphically. The results show that the variable thermal conductivity and diffusivity as well as memory-dependent parameters have the varying degrees of influences on the structural transient thermo-elasto-diffusive responses. [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]

The size-dependent effect arising in micro/nano-structures has attracted considerable attention in academic and industrial communities. The theories developed to characterize such effect mainly include the nonlocal elasticity theory, the strain gradient theory, the modified coupled stress theory and the more recent nonlocal strain gradient elasticity etc. Meanwhile, the thermal-induced deformation or stress in micro/nano-structures is increasingly becoming a vital issue in their designs and applications. Nevertheless, theoretical investigations to predict the thermoelastic performances of micro/nano-structures are not so common, especially in the case of nonlocal strain gradient elasticity incorporating thermoelastic coupling effect. In present work, investigation of thermoelastic wave propagation in micro-beam is conducted in the context of the nonlocal strain gradient elasticity and the G-N theory, taking the thermoelastic coupling effect into account. The governing equations are formulated based on the Euler–Bernoulli beam model and the G-N theory. By assuming the wave-type solutions, the equations are solved and the dispersion relation between frequency and wave number and the relation between phase velocity and wave number are determined respectively. In calculation, the above two relations are fully investigated and comparisons on them under different theories are provided accordingly. Some new findings are presented and discussed in detail. It is hoped that the present work may provide some guidelines in designing and optimizing micro-structures. [ABSTRACT FROM AUTHOR]

In extreme heat transfer environments, functionally graded materials (FGMs) have aroused great concern due to the excellent thermal shock resistance. With the development of micro-scale devices, the size-dependent effect has become an important issue. However, the classical continuum mechanical model fails on the micro-scale due to the influence of the size-dependent effect. Meanwhile, for thermoelastic behaviors limited to small-scale problems, Fourier's heat conduction law cannot explain the thermal wave effect. In order to capture the size-dependent effect and the thermal wave effect, the nonlocal generalized thermoelastic theory for the formulation of an FGM microbeam is adopted in the present work. For numerical validation, the transient responses for a simply supported FGM microbeam heated by the ramp-type heating are considered. The governing equations are formulated and solved by employing the Laplace transform techniques. In the numerical results, the effects of the ramp-heating time parameter, the nonlocal parameter, and the power-law index on the considered physical quantities are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

Summary: Nanoscale piezoelectric energy‐harvesting from ambient vibration sources has great potential for practical applications in powering nanoelectronic and nano‐wireless sensors. Nowadays, the piezoelectric laminated sandwich smart nanocomposites have been extensively applied as nanogenerators, nano‐energy harvesters, and the other nano‐electromechanical devices. However, no works have thoroughly investigated the size‐dependent dynamic thermo‐electromechanical response of such structure that consider the perfect/non‐idealized interfacial conditions and piezoelectric material constants ratios. This article will address this problem based on the size‐dependent piezoelectric thermoelasticity theory by a semi‐analytical technique via the Laplace transformation. If the thermal/elastic nonlocal parameters or material constants ratios are properly selected, the results show that: (a) the electrical energy harvesting and heat isolation can be maximally improved; (b) the harmful thermal stresses will be lowered to some extent. This work not only provides a thorough and comprehensive understanding on response of piezoelectric laminated sandwich smart nanocomposites serving in non‐uniform thermal environment, but also offers basic guidelines for its thermal management and piezoelectric energy harvesting. [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]

Nowadays, a multilayered viscoelastic composite structure stands as one of the most representative active/passive vibration isolator and high-efficient damper to avoid unwanted vibrations in civil and ocean engineering, which is commonly applied in harsh non-uniform temperature environment (e.g., high heat-flux, drastic changes of temperature, etc.). In such a case, thermoviscoelastic response analysis is of great importance for the safety design of viscoelastic composites, and so a thorough and comprehensive study on this issue is imperatively needed. This work aims to conduct an analytical study of transient thermomechanical responses of multilayered viscoelastic composite structure under time-dependent heating loads. In the context of generalized thermoviscoelasticity theory with time-fractional order strain, a composite laminated viscoelastic plate is chosen as the analytical model while governing equations of each homogeneous layer accounting for non-idealized interfacial conditions are systematically formulated. Then, a semi-analytical approach via Laplace transform is adopted to deal with the problem. The effects of fractional order parameters and material constants' ratio on the structural dynamic responses are fully discussed to provide new insights and basic guidelines for vibration control and thermal management of viscoelastic composites, especially for the surface coating at the interface between any two adjacent viscoelastic layers. [ABSTRACT FROM AUTHOR]

Piezoelectric materials have become one of the most promising candidates for a new class of smart structures which are widely used as sensors and actuators in control systems due to their superior electromechanical performance and high‐efficiency in electro‐mechanical energy conversion. In recent years, although there are many papers of theoretical modeling of generalized piezoelectric thermoelasticity that considered the piezoelectric‐thermoelastic coupling of piezoelectric structures serving in the extreme fast heating environment (e.g. ultra‐fast laser), the strain relaxation effect has not been considered yet. This work aims to investigate the generalized piezoelectricity problem with strain rate with the aid of extended thermodynamic principles, and corresponding generalized variational theorem is also strictly formulated to provide a complete rationale for numerical method by using semi‐inverse method. For numerical evaluation, transient thermo‐electromechanical responses of a one‐dimensional semi‐infinite piezoelectric medium with one end subjecting to a sudden thermal loading are considered and solved by applying Laplace transformation methods. Then the transient responses of temperature, displacement, strain, stress and electric potential are obtained and illustrated graphically, and the influences of strain relaxation parameters on them are also analyzed and discussed. [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]

Based on the generalized thermoelastic diffusion theory with fractional order derivative, the dynamic response of an infinite thermoelastic medium with a spherical cavity is investigated. The thermoelastic and diffusive properties of the medium are assumed to be temperature-dependent, and the medium is subjected to a thermal shock and a chemical potential shock at the inner surface of the spherical cavity simultaneously. The governing equations of the problem are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, radial stress, concentration and chemical potential are obtained and illustrated graphically. In calculation, the effects of the fractional order parameter and the temperature-dependent properties on the variations of the considered variables are presented and discussed in detail. The results show that the fractional order parameter and the temperature-dependent properties significantly influence the variations of all the considered variables. The present investigation may be valuable in heat and mass transfer, waste disposal or petroleum engineering, etc. [ABSTRACT FROM AUTHOR]

In this work, we shall formulate the fibre-reinforced two-dimensional problem of thermoelasticity for an infinite space weakened by a finite linear opening mode-I crack. In the context of the fractional order theory of generalized thermoelasticity proposed by Sherief et al., we focus on investigating the dynamic response and the governing equations of the problem are formulated and solved by means of normal mode analysis. The distributions of the considered non-dimensional temperature, displacement and stress are obtained and illustrated graphically. The effects of fractional order parameter, rotation, crack dimension on the variations of the considered variables are investigated, and the results show that this parameter has significant influence on the variations of the considered variables. [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]

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]

The dynamic response of a two-dimensional generalized thermal shock problem is investigated in the context of the fractional order theory of thermoelasticity proposed by Sherief et al. To demonstrate the solution process, a thermoelastic half-space subjected to a thermal shock on its bounding surface is considered in detail. The governing equations for the problem are formulated and then solved by normal mode analysis. The distributions of the considered nondimensional temperature, displacement, and stress are obtained and illustrated graphically. The effect of fractional order parameter on the variations of the considered variables is investigated, and the results show that the fractional order parameter has significant influence on the variations of the considered variables. [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]

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]

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]

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]

The Stefan conditions are suitable for describing the solid-liquid phase change processes with moving interface. However, the existing literature only focuses on the Stefan problem of heat conduction and does not involve the thermo-mechanical coupling effects. In this work, the generalized thermoelastic Stefan problem with spatio-temporal nonlocal effect is investigated. The solid-liquid phase change of silicon with picosecond pulse laser machining is depicted by the Stefan interface conditions. We find the solutions making use of Laplace transformation and Laplace numerical inverse transformation. The temperature distribution at the moment of surface melting is seen as the initial state of the second phase. The distributions of transient thermoelastic responses under different laser intensities, pulse widths, fractional order parameters, spatial nonlocal parameters and time are obtained and expressed graphically. • The introduction of Stefan conditions into the nonlocal generalized thermoelasticity. • The solid-liquid interfaces moving with time due to laser processing are considered. • The temperature at the surface melting moment is taken as the initial condition. • The heat taken away by vaporization is considered in the boundary condition. • With laser intensity increasing/duration decreasing, the transient responses increase. [ABSTRACT FROM AUTHOR]

In recent years there have been many papers that considered the pyroelectric effect in the investigations of thermo-mechanical coupling of piezoelectric ceramics serving in non-uniform thermal environment, particularly with extensive applications of ultrafast heating technologies (e.g., laser burst, laser ablation, etc.) in micro-machining of piezoelectric structures (e.g., piezoelectric sensor/actuator/generator/energy harvester, etc.). However, in such conditions, the existing piezoelectric thermoelasticity theories will not be applicable due to the lack of consideration of the memory-dependence feature in the constitutive relations and heat transport equation. To further refine the piezoelectric thermoelasticity models, present study develops a new theoretical model of generalized piezoelectric thermoelasticity which fully account for fractional order strain and heat conduction. By establishing constitutive equations within the extended thermodynamic framework, the governing equations are derived. In the aspect of application, the transient thermo-electromechanical responses of multi-layered piezoelectric laminated composite structure with non-idealized interfacial conditions is investigated. The effects of material constants ratio and fractional order parameters of each layer on structural responses are evaluated and summarized to offer some new insights and guidelines on the strength design, thermal protection, and vibration control of multi-layered piezoelectric laminated composite structure under ultrafast heating condition. • New theoretical model of piezoelectric thermoelastic coupling is developed. • An analytical model of multi-layered piezoelectric laminated structure is chosen. • Non-idealized interfacial conditions are considered. • Transient thermo-electromechanical responses are investigated. • Material constants ratio and strain relaxation show great effects on responses. [ABSTRACT FROM AUTHOR]

In recent years, extensive studies on carbon nanotubes-reinforced composites (CNTRC) and graphene platelets-reinforced composites (GPLRC) have been conducted primarily within the framework of the classical elasticity or thermoelasticity. However, there lacks of researches on the thermoelastic behaviors of CNTRC/GPLRC structures based on the generalized thermoelasticity considering non-Fourier heat conduction, especially lacking of studies that address the microstructures of these materials incorporating nonlocal effects. To address this gap, this work applies the generalized thermoelastic theory, which incorporates dual-phase thermal relaxations, thermal nonlocality and elastic nonlocality, to investigating the thermoelastic vibration characteristics of a nanocomposite microbeam reinforced by both GPLs and CNTs. The Halpin–Tsai micromechanical model is used to evaluate the effective elastic modulus of the composite microbeam, which is then analyzed using the Euler–Bernoulli beam model and solved via Navier’s method to determine the natural frequency. In calculation, the unidirectional distribution and three different functionally graded (FG) distributions of CNTs and GPLs, i.e., FG-A, FG-X and FG-O and also the influences of the nonlocal parameters, the volume fraction indices and the mass fractions of GPLs and CNTs on the natural frequencies are examined. The obtained results show that FG-A type significantly influences the natural frequency. The inclusion of GPLs and CNTs in the epoxy resin matrix markedly increases the natural frequency of the microbeam, with hybrid reinforcement being superior to GPLRC and CNTRC. The nonlocal elasticity parameter negatively correlates with the natural frequency, while the mass fraction and volume fraction index of GPLs and CNTs positively correlate with the natural frequency. [ABSTRACT FROM AUTHOR]

Abstract: By using the principle of virtual work, the finite element equations corresponding to the generalized thermoelasticity with two relaxation times (i.e., the G–L theory) are derived. In order to improve the accuracy of integral transform method, especially in two/three-dimension, the equations are solved directly in time-domain. As numerical examples, the developed method is used to investigate the generalized thermoelastic behavior of a slim strip and a semi-infinite plate subject to thermal shock loading. The results demonstrate that the developed method can faithfully predict the deformation of the structure and most importantly the delicate second sound effect of heat conduction in both one and two-dimensional solids whilst it is usually difficult to model, especially in two-dimensional, by using the transform method. This method can also be used to study generalized piezothermoelastic and magnetothermoelastic problems. [Copyright &y& Elsevier]

In present paper, a linear thermoelastic theory for porous materials is established by extending the existing theory, in which the strain relaxation and the thermal relaxation are included. Based on the thermodynamic laws, the constitutive relations are derived, and then the corresponding constitutive equations are obtained by specifying the generalized free energy. Further, by combining the existing theory, the non-Fourier's heat conduction law and the obtained constitutive equations, the linear thermoelastic theory for porous materials is formulated. To apply the established theory, the transient response of a half-space with voids is considered. The half-space with voids is subjected to a thermal shock and a mechanical shock simultaneously on its bounding surface. The problem is solved by means of Laplace transform and its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress as well as the volume fraction field are obtained and illustrated graphically. In calculation, the effects of the thermal relaxation factor, the strain relaxation factor and the magnitude of the mechanical shock on the considered variables are examined and discussed in detail. • A new linear thermoelastic theory for porous materials is established by extending the existing theory. • The main novelty of this new theory lies in that both the strain relaxation and the thermal relaxation are included. • This new theory is formulated by means of thermodynamic laws and work-energy relation. • The application of this new theory to the thermoelastic dynamic response of a half-space with voids is presented. [ABSTRACT FROM AUTHOR]

The studies of the coupling of thermodiffusion and mechanical deformation in solids have aroused great interests with miniaturization of the micro/nano-electromechanical devices and wide application of ultrafast heating technologies. In such situation, it is commonly accompanied with high heat/diffusion flux and thermal/diffusion induced stress accordingly. So far, although there have been many developments and extensions of research and theorizing within the generalized thermoelastic diffusion problems, these theoretical formulations are only applicable when the strain rate is assumed to be relatively small, but this is questionable under ultrafast heating condition. The present work aims to investigate generalized thermoelastic diffusion problems with fractional order strain within the extended thermodynamic framework. For numerical evaluation, the analytical model of a sandwich structure with ideal interfacial conditions is investigated whilst its bounding surfaces are subjected to symmetrical transient heat and chemical potential shock loads. From numerical results, the effects of the fractional order parameters and material characteristic parameters of each layer on structural transient thermo-elasto-diffusive responses are also analyzed and discussed, which is expected to provide a comprehensive understanding on thermoelastic diffusive coupling and optimal design of sandwich structures under extreme fast heating condition. • Generalized thermoelastic diffusion theory with fractional strain is developed. • Transient thermoelastic diffusion responses of sandwich structure are studied. • Fractional order strain can characterize the strain relaxation feature. • Fractional order parameters have great effects on structural responses. [ABSTRACT FROM AUTHOR]