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Graphene nanoplatelets (GPLs) are considered to be a desirable reinforcing nanofillers for nanocomposite materials owing to their superior thermo‐mechanical properties. Meanwhile, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high‐performance micro/nano‐resonators. Nevertheless, the classical TED models fail at the micro/nano‐scale due to without considering the influences of the size‐dependent effect and the thermal lagging effect. The present work focuses on investigating TED analysis of functionally graded (FG) microplate resonators reinforced with GPLs based on the modified coupled stress theory (MCST) and the Moore–Gibson–Thompson (MGT) 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 mechanical properties of the plate‐type nanocomposite are evaluated based on the Halpin–Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the closed‐from analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length‐scale parameter, the thermal phase lag of the heat flux and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This results provide a more reasonable theoretical approach to estimate TED in the design of FG microplate resonators reinforced with GPLs with high performance. [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]

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]

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]

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]

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]

Thermoelastic damping is a significant energy dissipation mechanism in nano-resonator, and exploring its feature would lay a foundation for designing high-quality nano-resonators. Due to the size-dependent effect and the non-Fourier heat conduction effect arising in structures in nanoscales, the traditional models may fail to characterize thermoelastic damping in nano-resonators. To further develop the thermoelastic damping model in small scales, a novel thermoelastic damping model is established in the present work based on the modified couple stress theory and the non-Fourier heat conduction law. Based on the novel model, the exact expression of thermoelastic damping is obtained by the complex frequency method. In calculation, the results are validated by degrading the present model to the classical model, and the effects of length scale parameters, boundary conditions, reference temperature, and vibration modes on thermoelastic damping are examined and discussed in detail. The obtained results show that the influence of the present model on the amount of thermoelastic damping and the critical thickness is significant in small scales. [ABSTRACT FROM AUTHOR]

For thermoviscoelastic behaviors limited to ultrashort laser pulse technologies, the Fourier's heat conduction law may fail; meanwhile, new models, e.g., the fractional-order heat conduction model, have been developed to modify Fourier's law. Furthermore, it is found that the fractional-order viscoelastic models fit well with the experimental data from relaxation tests. Meanwhile, with the miniaturization of devices, the size-dependent effect on elastic deformation is becoming increasingly important. This paper addresses the transient thermoviscoelastic response of a polymer micro-rod subjected to an ultrashort laser pulse heating including the simultaneous effects of the fractional order parameter and the nonlocal parameter for the first time. The governing equations are obtained and solved by the Laplace transform method. In calculation, the influences of the magnitude of the laser intensity, the fractional-order parameter and the nonlocal parameter on the variation of the considered variables are analyzed and discussed in detail. It is hoped that the obtained results will be helpful in designing the viscoelastic micro-structures induced by a short-pulse laser heating. [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]

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]

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]

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]

• 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]

• 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]

Thermoelastic damping (TED) is one of the key factors for lowering the quality factor (Q-factor) of micro/nano-resonators. However, due to a complex small-scale effect and governing equations of non-homogeneous isotropic materials, the existing TED models usually focus on homogeneous isotropic micro/nano-resonators. In this paper, a closed-form TED model is derived to estimate the influence of the small-scale effect on TED of transversely isotropic micro/nano-resonators. The surface effect and the dual-phase-lag model are included to distinguish the influence of mechanical and thermal small-scale effects on TED, respectively. The obtained TED model is theoretically verified. The results indicate that TED values are underestimated if the classical TED model is employed. Moreover, a critical thickness can be determined by the frequency shift curve is proposed. The small-scale effect results in higher TED values within the critical thickness. However, since the small-scale effect has a weak influence on TED, it can be neglected when the resonator thickness is higher than the critical thickness. Additionally, the surface effect plays a dominant role in improving the TED of nano-resonators. In this paper, a more reasonable theoretical approach for estimating TED in transversely isotropic micro/nano-resonators is provided. [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]

• Ultrashort laser has obvious impacts on the heat conduction and structural response. • Comparison of results between the fractional order and memory dependent derivative. • The obtained curves agree well with the previous theoretical deduction. • The bigger contact thermal resistance leads to the larger mutation at the interface. • Kernel function and material characteristic have marked impacts on the variables. Ultrashort laser technology has been widely used in micro-machining due to its high power, precision of operation, low cost, high control and extremely short duration. This motivates us to investigate the transient response of a bi-layered structure subjected to a non-Gaussian laser beam on its bounding surface in the context of the time-fractional derivative based on generalized thermoelastic theories. Comparison studies between the fractional order and the memory-dependent derivative models are performed and the thermal contact resistance at the interface is also considered. The coupled governing equations involving with thermal relaxation time, fractional order parameter, time delay and kernel function, which can be chosen freely according to specific problems, are solved by using Laplace transform technique together with its numerical inversion. During the analysis, the first layer is selected as the copper material and the material characteristic parameters of the second layer such as the thermal conductivity, mass density and specific heat capacity are given by ratios to those of the first layer. The influences of the material characteristic parameters on the heat conduction and the structural responses are emphatically discussed, and the non-dimensional temperature, displacement as well as stress at different values of fractional order parameter, time delay factor, kernel function and thermal contact resistance are obtained and illustrated graphically. Finally, based on the obtained results, the bi-layered structure heated by a non-Gaussian laser beam may be reasonably designed in engineering. [ABSTRACT FROM AUTHOR]