Influence of the mechanical damage on vibration of a viscothermoelastic circular microplate resonator based on dual-phase-lag heat conduction

Abstract

We establish a mathematical model of thermally conducting an isotropic, homogeneous, and circular microplate in the context of Kirchhoff’s Love plate theory. We define the governing equations in the context of the generalized dual-phase-lagging model and coupled viscothermoelastic plate. We illustrate the scaled viscothermoelasticity for the case of a circular plate for an aspect ratio for clamped boundary conditions. The bounding plane of the plate has been thermally shocked by ramp heating. We apply the Laplace transform and numerically calculate its inversions. The results are obtained for a ceramic plate. The effects of the damage variables and the thickness of the resonator on the temperature increment distribution are found to be minimal, whereas the effect of the ramp heat parameter on the temperature increment is significant. The damage variables and the thickness of the resonator have significant effects. We determine that the ramp heat parameter can be used as a controller to tune the energy damping.