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With their abilities to induce electric charge, stress or deformation in response to external forces as well as the ease of fabrication, design flexibility and excellent electromechanical properties, piezoelectric materials have been widely used in actuators, sensors and even in nano/micro-electro-mechanical systems. With the rapid advancement of nano/micro-technology, from the perspective of theoretical analysis, the priority is to develop applicable models to describe the piezoelectric-thermoelastic responses of piezoelectric nano/micro-structures suffering transient heat conduction by taking the size-dependent effect and the memory-dependent effect into consideration. In this work, a new model based on the existing piezoelectric-thermoelastic model is established by introducing the nonlocality into the constitutive equations and the memory-dependent derivative into Moore-Gibson-Thompson (MGT) heat conduction equation respectively. Then, this new model is applied to investigating the dynamic responses of a piezoelectric nanoplate subjected to thermal shock. The corresponding governing equations are formulated and then solved by Laplace transform and its numerical inversion. In calculation, the influences of the time delay factor and the kernel function of MDD and the non-local parameter on the thermal, electric and elastic fields in the piezoelectric nanoplate are examined. Meanwhile, the predictions of transient response among different thermoelastic models are compared. The numerical results are illustrated graphically and discussed in detail. The obtained results show that MDD has a significant effect on the transient response, where the effect of the kernel function is more pronounced. This work may provide a theoretical reference for strength design, thermal protection and thermal processing strategies for piezoelectric nanodevices. [ABSTRACT FROM AUTHOR]

Functionally graded sandwich micro/nano-structures have attracted great attention due to the capability to resist high noise and thermal stress in a non-isothermal environment. Additionally, the design of high quality-factor micro/nano-resonators requires accurate estimation of their thermoelastic damping. However, the classical thermoelastic damping models fail at the micro/nano-scale due to the influences of the size-dependent effects related to heat transfer and elastic deformation. This work aims to investigate the influences of the size-dependent effects on the thermoelastic damping of functionally graded sandwich micro-beam resonators by combining the nonlocal dual-phase-lag heat conduction model and the nonlocal elasticity model. It is assumed that the functionally graded sandwich micro-beam resonators consist of a ceramic core and functionally graded surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of thermoelastic damping is obtained by complex frequency method. Numerical results are analyzed for the effects of the thermal nonlocal parameter, the elastic nonlocal parameter, the power-law index, and the vibration modes on the thermoelastic damping of functionally graded sandwich micro-beam resonators. The results show that the thermoelastic damping of functionally graded sandwich micro-beam resonators can be adjusted by the suitably modified parameters, which strongly depends on the double nonlocal effects and the power-law index. [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]

Ultra-slow relaxation process of polymers has the memory-dependent feature, integer-order thermoviscoelastic models may fail to describe the dynamic behaviors of viscoelastic structures accurately. Additionally, it is noticed that the small-scale effect of elastic deformation and heat conduction in a non-isothermal temperature environment is becoming significant due to the development of micro-devices. To better capture the memory-dependent effect and the small-scale effect of viscoelastic micro-structures in heat transfer environment, as a first attempt, present work focuses on developing a refined fractional Kelvin-Voigt thermoviscoelastic model by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). Then, the model is applied to investigating the transient response of a polymer microbeam subjected to a harmonic thermal loading. The governing equations involving the modified parameters are formulated and then solved by Laplace transform method. Some parametric results are demonstrated to display the impacts of the nonlocal thermal parameter, the material length-scale parameter and the fractional-order parameter on the considered physical quantities. The results show that the small-scale effect and the memory-dependent effects strongly depend on the polymer micro-structure characteristics in thermal environment. [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]

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]