Viscothermoelastic vibrations on circular microplate resonators using the Moore–Gibson–Thompson thermal-conductivity model

Abstract

This research investigates the impact of thermoelastic coupling on thermally conducting, homogeneous, and isotropic Kelvin–Voigt-type circular microplate resonators. The study utilizes the Moore–Gibson–Thompson technique, which incorporates viscous effects. We examine the use of clamped boundary conditions and obtain analytical solutions in the Laplace-transform domain. In order to clarify the thermomechanical effects on the vibrations of a ceramic Si₃N₄ plate resonator, we calculate numerical outcomes in the time domain by employing the inverse Laplace transform. We examine the impact of viscosity on many physical phenomena, including deflection, temperature, displacement, thermal moment in the radial direction, and radial stress. We give graphical findings that compare the results with and without the presence of viscosity. The study evaluates the precision and feasibility of the MGTE thermal-conductivity theory by comparing its numerical outcomes with well-established thermoelastic models, such as the classical theory, Lord–Shulman theory, and Green–Naghdi II and III theories. The MGTE theory showcases improved accuracy, facilitating the production of circular micro/nanoplate resonators with exceptional quality and decreased energy dissipation.