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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]

High-Q micro-beam resonators have been widely applied in communication fields such as narrowband filters, but thermoelastic damping restricts the further improvement of quality factor. Traditional method such as overall size optimization used for thermoelastic quality factor (QTED) improvement will cause the resonant frequency of the resonator change greatly, which will not be allowed in narrowband filters. In this article, three slots are introduced into a beam resonator to greatly reduce the thermoelastic damping by rationally arranging the length ratio of the central slot and the side slot, while the resonant frequency is basically kept unchanged. The feasibility is verified by parametric finite element simulation method. The results indicate that without changing the overall size of the micro-beam resonator, the resonant frequency remains unchanged and the QTED of the resonator can be doubled over twice both in the isothermal region and adiabatic region by placing side slots of 10% and a central slot of 30%. The proposed thermoelastic damping suppression method shows potential applicability for MEMS resonators in high-order mode of vibration. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) has been confirmed as an intrinsic energy loss and determines the upper limit of the quality factor of micro/nanoelectromechanical system (M/NEMS) resonators. A framework for determining the TED in the full clamped (C-C-C-C), clamped-free-clamped-free (C-F-C-F), and cantilever (C-F-F-F) rectangular microplate resonators operating in the fundamental mode by considering three-dimensional heat conduction in conjunction with modified couple stress theory (MCST) is proposed in this article. Then by using Rayleigh's method, three analytical models expressed by Fourier series for TED are derived, respectively. The difference between the present TED model and the previous one-dimensional (1-D) MCST model and 3-D classical model are comprehensively investigated. The comparison results indicate that the size effect on TED decreases to be ignorable as the thickness increases to h/l ≥ 50. In the case of h/l ≤ 50, the size effect cannot be ignored. The corresponding critical thicknesses for TED peaks are independent of the size effect. TED behaviors vary significantly under different structural support types. [ABSTRACT FROM AUTHOR]

This manuscript studies thermoelastic damping of a longitudinally vibrating nanorod at small-scale. The heat conduction in the present work is constructed based on the three phase-lag heat conduction model and the elastic effects are modeled using nonlocal elasticity. Isothermal and adiabatic type of thermal boundary conditions are considered in the numerical analysis. It is found that the thermoelastic damping of the present resonator under adiabatic thermal boundary conditions is higher than that of the isothermal boundary conditions. The nonlocal elasticity gives higher thermoelastic damping than the classical elasticity. The present results are in good agreement with those of the available literature. Thermoelastic damping for clamped-clamped nanorod vibrating in longitudinal mode is 83% higher than that of the clamped-free nanorod for both adiabatic and isothermal boundary conditions. The critical length of nanorod at which the thermoelastic damping is maximum, is lower for the adiabatic condition than isothermal condition. The energy dissipation occurs at very fast rate at higher values of thermal relaxation parameters and more clearly this effect is seen for nanorod with less than 100 nm length. The numerical results presented in this work are useful for the design of the next generation nanoscale devices based on longitudinal resonators. [ABSTRACT FROM AUTHOR]

Size effect is a significant factor for accurate estimation of the thermoelastic damping (TED) in microplate/nanoplate resonators. The actual TED in microstructures/nanostructures is comprehensively affected by various size-dependent mechanisms in the mechanical and thermal field and studying only one of them may lead to one-sided conclusions. In this article, the governing equations of coupled thermoelasticity in a transversely vibrating rectangular plate are derived by the modified nonlocal strain gradient theory and the nonlocal heat conductive law (GK model). Then utilizing the energy approach, a size-dependent TED model for rectangular plates is presented in the form of infinite series. The constitutive boundary conditions are considered to close the nonlocal strain gradient problem in differential form. The silicon material with typical length scale parameters and relaxation time is selected in simulation. The influences of nonlocal elasticity, strain gradient elasticity and nonlocal heat conduction on TED in rectangular plates are investigated under different frequencies, thicknesses and boundary conditions. The simulation results show that the TED expression converges rapidly and the three size-dependent parameters have distinct influences on TED value, critical thickness and critical frequency. By taking advantage of the size effects reasonably, the quality of resonators can be improved. [ABSTRACT FROM AUTHOR]

Thermoelastic damping is a prominent internal dissipation mechanism in small-scale mechanical resonators. It has been given a lot of attention recently due to the endeavors to design high-quality nanoelectromechanical systems. In the article, this phenomenon is analyzed for in-plane vibration of orthotropic and isotropic nanoplate resonators using coupled nonlocal heat conduction and nonlocal elasticity theories. The obtained thermal-displacement equations are solved using the Galerkin residual technique and the output results are illustrated and compared for isotropic and orthotropic materials, using the classical theory, the nonlocal elasticity theory, the nonlocal heat conduction theory, and coupled nonlocal thermoelasticity. The results show significant impacts of both the nanosystem geometrical and physical parameters on the quality factor. [ABSTRACT FROM AUTHOR]

We explore the analysis of exact three-dimensional free vibrations of visco-thermoelastic solid cylinder, which has been considered at a uniform temperature and undeformed initially in the framework of generalized thermoelasticity. The formulation has been implemented with two relaxation time parameters, i.e., mechanical and thermal relaxation parameters. The series solution has been implemented to solve the differential equations along with the evaluation of stresses, displacements, and temperature by applying stress-free, rigidly fixed, thermally insulated and isothermal boundary conditions. The relations of frequency equations for the existence of different modes of visco-thermoelastic solid cylinder have been developed in compact form using assumed boundary conditions. Thermoelastic damping and frequency shift are presented graphically from the data generated by computations and simulations of numerical results. Also, the natural frequencies are represented in the form of tables which show that with an increase in the ratio of length to the radius and axial wave-number, the variation of vibrations keeps increasing. [ABSTRACT FROM AUTHOR]

In this article, the constitutive relations and the governing equations are derived for nonlocal thermoelastic solid in the presence of diffusion. The free vibration of a thermoelastic diffusive cylinder is investigated within the framework of the above newly derived model. Time-harmonic vibration is used to transform the governing equations into a system of ordinary differential equations. The frequency equation is taken under investigation for the survival of a range of possible modes in compact form for traction-free thermal boundary conditions: thermally insulated and isothermal boundary conditions. To explore the vibration analysis from frequency equations, we apply a numerical iteration technique for generating numerical data by taking assistance of the Matlab software. The numerically computed and simulated results for the frequency shift, natural frequency, and the thermoelastic damping are presented graphically. The effect of nonlocality on the above quantities is observed and shown graphically. [ABSTRACT FROM AUTHOR]

This paper deals with the small-scale effects on the thermoelastic damping (TED) in microplates. The coupled equations of motion and heat conduction are provided utilizing the strain gradient theory (SGT) and the dual-phase-lag (DPL) heat conduction model. Solving these equations and adopting the Galerkin method, the real and imaginary parts of frequency are extracted. The complex frequency approach is then employed to present a size-dependent expression for evaluating TED in thin plates. An analytical expression for TED incorporating small-scale effects is also derived on the basis of the energy dissipation approach. To survey the effect of different continuum theories on TED, the results obtained by SGT are compared with those predicted by the modified couple stress theory (MCST) and the classical continuum theory. Furthermore, through a number of parametric studies, the effects of some variables on the amount of TED, such as microplate thickness, type of material and boundary conditions are discussed. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) is one of the main energy dissipation mechanisms in micro/nano resonators and one of the major concerns in respect to performance of micro-electromechanical systems and nano-electromechanical systems devices. In this article, we report that application of pre-tension stress on micro/nano circular plate resonators not only increases the resonant frequency, but also reduces TED. Analytical expressions of TED in micro-plate resonators, subjected to uniform radial pre-tension stress around its edge, are derived by means of thermal energy method. Thermal conductions along both the thickness direction and the radial direction are taken into account. TED obtained by using 2-D thermal conduction model is expressed in the form of infinite series and the convergence of the series is also discussed. Numerical results show that application of pre-tension is able to considerably reduce TED of micro-plate resonators. The effects of the dimensions, ratio of thickness to radius and vibration modes of circular plate resonators on TED are examined. This study indicates that application of pretension in micromechanical resonators could be a viable means to modulate resonant frequency and TED. [ABSTRACT FROM AUTHOR]

It has been reported that application of tensile axial stress can simultaneously increase quality factor and resonant frequency for micromechanical resonators. In this study, we formulate an analytical model for evaluating thermoelastic damping in micromechanical resonators based on the thermal energy method, in which thermal conductions in both thickness direction and axial direction are considered. An explicit expression for thermoelastic damping in the form of infinite series has been obtained. The proposed analytical model is further validated by finite element analysis. Results of the present study demonstrate that the 2D model needs to be adopted in order to accurately evaluate thermoelastic damping of micromechanical resonators with axial pretension. In addition, the 2D model proposed in the present study eliminates the inherent inconsistency entailed in the 1D model. [ABSTRACT FROM AUTHOR]

The present article investigates the quality factor of thermoelastic damping in micro-beam resonator from the standpoint of a very recent thermoelasticity theory proposed by Quintanilla (2011). In recent years, significant attention is being paid to micro- and nano-resonators due to their wide applications in micro- and nano-electromechanical systems (MEMS/NEMS). The quality performance of a micro-beam resonator is usually measured by the quality factor and thermoelastic damping is considered to be the most important intrinsic dissipative mechanism in micro and nanoscale devices. In the present article, we consider the heat conduction model with a single delay term given by Quintanilla (2011) and derive an expression for thermoelastic damping by applying complex frequency approach. The variation of thermoelastic damping versus normalized frequency and thickness of Silicon micro-beam resonator for different aspect ratios have been studied. We compare the results of present model with the corresponding results of thermoelasticity theories of type GN-III, three-phase-lag (TPL), and Lord-Shulman (LS) models and investigate that the new model with a single delay term (NMSDT) gives high Q-factor of the micro-beam resonator's sensitivity in comparison to LS and TPL models and the results under this model have more similarity to the results of GN-III model. [ABSTRACT FROM AUTHOR]

In this article, the size-dependent behavior of micro-beams with the thermoelastic damping (TED) phenomenon is studied. The coupled thermoelasticity equations are derived on the basis of the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model. By solving these coupled equations simultaneously, a closed-form expression for the TED parameter in micro-beams is presented which considers the small-scale effects incorporation. Then, the effect of various parameters on TED in micro-beams, such as micro-beam height, the type of material, boundary conditions, and aspect ratio is investigated. The results show that the influence of utilizing non-classical continuum and thermoelasticity theories on the amount of TED and the critical thickness is significant in small scales. [ABSTRACT FROM AUTHOR]

The fundamental characteristic of mechanical resonators can be evaluated by resonance eigenfrequency and energy dissipation (or inverse quality factor). Reduced length scales are necessary for achieving high resonance eigenfrequency, which can afford fast response and extraordinary sensitivity to external forces. However, smaller scales will result in higher energy dissipation (or smaller quality factor) in the eigenfrequency of mechanical resonators. A topology optimization process is presented for enlarging quality factor of a microbeam resonator made of linear, isotropic and homogeneous thermoelastic material. The beam's width is supposed to be considerable so that the plane strain assumption can be satisfied and the design domain is the cross section along the beam's thickness. By combining the equation of motion and the heat transfer equation, the damping problem of thermoelastic coupling can be solved by a finite-element method. A topology optimization method is used to enlarge quality factor in microbeam resonators. It is found by clamped-clamped and clamped-free microbeam resonators that significant improvements of quality factors can be achieved through this optimization process. [ABSTRACT FROM AUTHOR]

In this article, thermoelastic damping (TED) in functionally graded material (FGM) circular micro plates is analyzed based on classical plate theory and one-way coupled heat conduction equation. The material properties are assumed to be varied continuously in the thickness direction of the plate. A one-way coupled heat conduction equation with variable coefficients is solved by using a layer-wise homogenization approach. The complex frequency, including TED, of the FGM micro plate is obtained in terms of the natural frequency of the corresponding isothermal homogenous plate without TED from the mathematical similarity between the eigenvalue problems of governing differential equations of the two kind structures. Numerical results of TED for a ceramic-metal composite FGM circular micro plate are presented quantitatively to show the effects of the material gradient index, the geometry, the vibration mode shapes, and the environmental temperature on the TED in detail. The present mathematical model and solution method can be also used to evaluate TED in the FGM circular and annular plates with other through-thickness material gradient forms. [ABSTRACT FROM AUTHOR]

Thermoelastic damping of nanobeams by considering the size effects of nanostructure and heat conduction is studied herein. The size effect of nanostructure is investigated based on Euler-Bernoulli beam assumptions in the framework of nonlocal strain gradient elasticity, and the size dependence of heat conduction is taken into account by incorporating phase-lagging and nonlocal effects. Closed-form solutions of thermoelastic damping and quality factor characterized by thermoelastic coupling are derived. Graphene nanoribbon is chosen as a nanobeam. The effects of relaxation time, aspect ratio, elastic modulus, thermal expansion, and thermal conductivity on quality factor of graphene nanobeams are discussed in detail. [ABSTRACT FROM AUTHOR]

The present article attempts to investigate thermoelastic damping (TED) of a microbeam resonator by employing the three-phase-lag (TPL) thermoelasticity theory proposed by Roychoudhuri. An explicit formula of TED has been derived and the effects of the beam height, the phase-lag parameters on TED of the microbeam resonator have been studied. Effects of beam height and phase-lags on TED have been shown with the numerical results. A comparison of the results with the corresponding results of the theory of thermoelasticity of type GN-III is also presented. It has been observed that GN-III predicts a high-quality factor of the resonator's sensitivity as compared to TPL model. [ABSTRACT FROM AUTHOR]

In this article, a model concerning free vibrations of spherically symmetric, thermoelastic, isotropic, and functionally graded sphere has been developed and analyzed in the context of linear theory of generalized thermoelasticity with one relaxation time. Laplace transform has been used to solve the problem which yields natural frequencies of free vibrations without performing inversion of the transform. The analytical results for coupled, uncoupled, and homogeneous spheres have been deduced as special cases of the general case. Natural frequencies of first 10 modes of vibrations have been obtained for different values of grading index of cobalt material regarding coupled thermoelastic, generalized thermoelastic, and elastic functionally graded spheres. The frequency shift and thermoelastic damping for Fourier and non-Fourier processes of heat propagation, temperature change, radial, and hoop stresses have been presented graphically. It has been analyzed here that grading index parameter helps in detecting the strength of signals in such material devices and the thermal relaxation time contributes in improving the quality of signals. The analysis also leads to the fact that grading index parameter is useful from design point of view and it can be tailored to specific applications for controlling the stress. [ABSTRACT FROM AUTHOR]