Papers by Keyword: Thermoelastic Damping

Abstract: In this paper, thermoelastic damping (TED) in a simply supported rectangular functionally graded material (FGM) micro plate with continuous variation of the material properties along the thickness direction is performed. The equations of motion and the heat conduction equation coupled with the thermal effects are derived based on the Mindlin plate theory and the one-way coupled heat conduction theory, respectively. The heat conduction equation with variable coefficients is solved by using the layer-wise homogenization approach. Analytical solution of TED is obtained by complex frequency method. Numerical results of TED are presented for the rectangular FGM micro plate made of ceramic-metal constituents with the power-law gradient profile. The effects of the shear deformation, the material gradient index, the plate thickness on the TED of the FGM micro plate are studied.

Abstract: Predicting thermoelastic damping is essential in the design of the next generation of layered composite microresonators. We present an analytical model for thermoelastic damping in circular microplates using the framework developed by Bishop and Kinra. The thermoelastic damping spectrum will exhibit two distinct peaks when the thermal conductivity of the substrate is much greater or less than that of the film. Increment of the thickness of a layer with the bigger Zener’s modulus will increase the peak damping.

Abstract: The paper concerns description of the thermoelastic phenomenon in an auxetic rectangular plate within the extended thermodynamical model. Analyzing vibrations of that plate a dependence of elastic constants on the frequency, particularly of Poissons ratio of auxetic state of the body has been presented. Moreover, considered investigations allow to determine the thermal relaxation time analyzing resonance frequencies of the vibrating plate.

Abstract: High quality factor is an essential requirement in the design of microsensors used for sensing and communications applications. In previous works, some analytical models have been developed for thermoelastic damping in monolayer structure and multi-layered beam. This paper proposes a new model for thermoelastic damping in symmetric, three-layered, laminated, microplate resonators. Our approach utilizes the analytical framework developed by Bishop and Kinra and Gaussian curvature. The effect of volume fraction is numerically calculated. It is noticed that the maximum damping is determined by volume fraction, which is independent of the single layer thickness. The thinner plate is, the higher frequency is that reach the maximum damping.

Abstract: In this paper, thermoelastic damping of the axisymmetric vibration of laminated circular plate resonators will be discussed. Based on the classical laminated plate theory assumptions, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of trilayered circular plate with fully clamped boundary conditions. The analytical expression for thermoelastic damping is obtained and the accuracy is verified through comparison with FEM results.

Abstract: In this paper, we present an analytical model for thermoelastic damping (TED) in micromechanical resonators, which is based on entropy generation, a thermodynamic parameter measuring the irreversibility in heat conduction. The temperature field of thin beam with small vibration is obtained by solving governing equations of linear thermoelasticity. The analytical solution is derived from the entropy generation equation. This method of entropy generation can provide an accurate estimation of the quality factor in flexural resonators. The results are compared with Zener’s approximation and LR (Lifshitz and Roukes) method. It is shown that the analytical model described in this paper is valid to estimate the quality factor due to thermoelastic damping.

Abstract: In this paper, a linear model of thermoelastic damping in annular microplate is considered for calculating the quality factor of this damping. In this model clamped boundary condition is applied in inner and outer circular edges. In the results, there are critical radius and thickness which are calculated analytically and in these dimensions, the thermoelastic damping becomes maximal. The critical radius and thickness depend on material properties, vibration modes and frequencies, dimensions of microplate.

Abstract: Predicting thermoelastic damping is crucial for the design of high Q MEMS devices. In the past, for the thermoelastic damping in microbeam resonators, Zener’s model (1937 Physical Review 52 230-5; 1938 Physical Review 53 90-9) and Lifshitz and Roukes’ model (2000 Physical Review B 61 5600-9) can give a reasonable prediction. However, the derivations of Zener’s model and Lifshitz and Roukes’ model are only suitable for a simple beam with no proof mass. The microbeam with a proof mass is a common element in many MEMS devices. In this paper, a general proof is presented that shows LR’s model is also valid for the TED in the microbeams with a proof mass. The derivation in this paper is based on a general case.