Thermoviscoelastic Responses in Kirchhoff Circular Micro-Plate via MGT Thermoelastic Model and Modified Couple Stress Theory

The study investigates thermal and elastic interactions in isotropic microplate resonators with elastic and viscous properties, exhibiting Kelvin–Voigt behavior, under a uniform magnetic field. Using the modified Moore–Gibson–Thomson thermoelastic theory (MGTE), modified couple stress theory (MCST) and the Hamiltonian principle, the differential equation of motion, including size effects, is derived. The model examines thermoelastic vibrations of a circular microplate with simply supported edges and various boundary conditions. The influence of length scale factors on the bending behavior of thermo-viscoelastic microplates is analyzed. Results show that microplates modeled with MCST theory are more rigid than those with standard continuum plate theory, aiding in the design of high-quality, low-energy-dissipation micro/nanosheet circular resonators. These findings are crucial for modern engineering, providing insights into thermoelastic coupling and enhancing microplate-based system performance and efficiency in various applications.