Vibration of Circular Microplate of Silicon Under Refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson Theorems of Thermoelasticity

Abstract This work presents novel unified mathematical models for analyzing the heat conduction of a circular micro-plate that is isotropic, homogenous, and thermoelastic. The models are based on Kirchhoff's Love of plate theory. The refined Green-Lindsay, Biot, Lord-Sulman, Green-Naghdi Type-1, Green-Naghdi Type-III, and Moore–Gibson–Thompson theorems of generalized thermoelasticity have been used under unified governing differential equations. The study demonstrates the application of scaled thermoelasticity to a circular microplate that is simply supported on the outer bounding surface. The microplate's bounding surface has been subjected to thermal loading using ramp-type heating, and the Laplace transform has been applied to the governing equations. Numerical calculations have been performed to determine the inverse of the Laplace transform by the iteration method of Tzou. The study included graphical comparisons between the studied models. The ramp-time heat, plate thickness, and parameters can be used as a tuner for the propagation of the thermomechanical waves through the silicon microplate. The closest models to each other in the mechanical behaviour are Green-Naghdi Type-III and Moore–Gibson–Thompson models, and then Biot of coupled thermoelasticity and Lord-Sulman of generalized thermoelasticity models.