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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]

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]

Achieving renewable power for self‐powered electronic devices such as micro/nano‐electro‐mechanical systems is attractive in the fields of energy resources and environment, in this regard, dielectric material structures with excellent energy storage and electromechanical responses have stimulated a surge of research interest. However, in the micro/nanoscale filed, the existing thermo‐electromechanical continuum theories are not capable of fully and effectively characterizing the arising effects, for example, size‐dependent effect and heat lagging effect, etc. To further develop the existing theories, a theoretical prototype for piezo‐flexoelectricity by incorporating strain gradient effect and dual‐phase‐lag heat conduction model is proposed for the first time in this study, and then this proposed model is applied to investigating the energy harvesting performances of a piezo‐flexoelectric micro‐beam under piezoelectric‐thermoelastic coupling. In terms of the differential form of two‐phase elasticity and Hamilton's principle, the governing equations and the boundary conditions for the transverse vibration of a micro‐beam based on the Euler–Bernoulli beam model are derived. By means of the assumed mode method, the influences of the flexoelectricity, the load resistance and the strain gradient on voltage and output power are examined. From the obtained results, it can be aware of that this study not only presents the piezoelectric‐thermoelastic coupling effect of piezo‐flexoelectric configuration in microscale field, but also presents that a piezo‐flexoelectric system at microscale can generate higher power than that reported in previous works. It is hoped that this study could provide some guidelines in designing and optimizing dielectric energy harvesters of micro/nano electronic 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]

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]

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]

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]

Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memory-dependent effect. Meanwhile, with the miniaturization of devices, the size-dependent effect on elastic deformation is becoming more and more important. To capture the memory-dependent effect and the size-dependent effect, the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the micro-scale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation, respectively. Then, the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source. The governing equations are obtained and solved by the Laplace transform method. In calculation, the effects of the fractional-order parameter, the fractional-order strain parameter, the mechanical relaxation parameter, and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail. [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]

• 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]

In this paper, from the view of active manipulation of electronic devices, to better reveal an external stimulus field-dependent mechanical tuning methodology and mechanism on the resonance characteristic and working performance, a comprehensive analytical model and theoretical solution of flexoelectric energy nanoharvester, driven via a time-harmonic magnetic field and thermal field, have been developed and established, in which, the coupled extensional and flexural vibration, flexoelectricity and surface effect as well as nonlinear magnetic-mechanical-thermo-electric coupling characteristic, are all included. After effective material constants of giant magnetostrictive material are exactly obtained, some key performance indexes (including strain gradient, output current, magneto-electric (ME) coupling coefficient, output power density, resonant frequency) of the harvesters are systematically investigated and discussed, which not only can be controled actively and tuned intelligently under applied external magnetic fields, pre-stresses and thermal fields stimuli, but also can also be dramatically enhanced and improved effectively through both flexoelectricity and surface effect. The theoretical model and solution obtained in this study are more general, which are suitable for the macroscopic and microscopic, linear and nonlinear mechanical analysises. Meanwhile, this work also provides a theoretical basis for more extensive investigations related to widely-used high frequency vibrations with shear deformation in device applications. [ABSTRACT FROM AUTHOR]