Vibration Analysis of Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation with Two Parameters Using the Moore–Gibson–Thompson Heat Conduction Model

This research aims to investigate the behavior of thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation using the Moore-Gibson-Thompson heat conduction equation, which is a newly developed method for studying heat transfer in elastic materials. The Moore-Gibson-Thompson (MGT) heat conduction model allows for a more accurate understanding of the thermoelastic vibrations in Micro-Beams. We aim to investigate how foundation parameters, and thermal relaxation times, influence vibration frequency and the stability of the micro-beam The Laplace transform method is used. The numerical solutions are represented graphically. The findings offer valuable insights for the design and optimization of micro-beams in advanced engineering applications, such as MEMS devices and nanoscale structures, where thermal effects and foundation interactions are crucial. Additionally, the variation of waves is slightly smaller in the case of the investigated