Vibration of circular micro-ceramic (Si3N4) plate resonators in the context of the generalized viscothermoelastic dual-phase-lagging theory

Abstract

In this article, the analysis and numerical results are represented for the thermoelastic of an isotropic homogeneous, thermally conducting, Kelvin–Voigt-type circular micro-plate in the context of Kirchhoff’s Love plate theory of generalized viscothermoelasticity based on the dual-phase-lagging model. The governing equations are obtained for the generalized dual-phase-lagging model and coupled viscothermoelastic plates. The scaled viscothermoelasticity has been illustrated in the case of the circular plate and the axisymmetric circular plate for an aspect ratio for clamped boundary conditions. Laplace transform has been applied, and its inversions have been calculated numerically by using the Tzou method. The results have been carried out for the ceramic (Si3N4). It is noted that the temperature increment and lateral deflection are significantly affected by the time, the width, the thickness, and the mechanical relaxation times of the material.