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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.

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.

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.

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.

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.

Due to the large voltage-induced strain along with other unique attributes, dielectric elastromers are being developed as transducers for broad applications in soft robots, adaptive structures, medical devices, energy harvesting and so on. Due to nonlinear large deformation and diverse modes of failure, it has been challenging to model dielectric transducers. This paper focuses on the optimization design of an actuator made of a layer of dielectric elastomer membrane and deformed into an out-of plane axisymmetric shape. The optimization procedure is demonstrated by examining the effect of three designing parameters, originated from the pre-stretch of the membrane, on the performance of the actuator, and by determining the region of allowable states in terms of several typical modes of failure. The equations of state are solved numerically by shooting method and the obtained numerical results indicate that the considered variables are sensitive to the designing parameters and that it is feasible to improve the performance of the actuator by choosing the designing parameters judiciously and averting the modes of failure. The approach presented here provides some guidelines in optimizing such actuators.