Viscoelastic Pasternak foundation analysis of a thermoelastic microbeam using Moore–Gibson–Thompson heat conduction under Klein–Gordon (KG) nonlocality

This study sought to examine the behavior of thermoelastic microbeams supported by a viscoelastic Pasternak foundation via the Moore–Gibson–Thompson heat conduction equation within the framework of Klein–Gordon nonlocality, a novel approach for analyzing heat transfer in elastic materials. This model facilitates a more precise comprehension of the thermoelastic vibrations in microbeams. We wanted to examine the impact of foundation characteristics and thermal relaxation durations on the vibration frequency and stability of the microbeam. The Laplace transform technique was used. A graphic representation of the computed temperature, bending displacement, and moment is shown. The results provide significant insights into the design and enhancement of microbeams in advanced engineering applications, including microelectromechanical systems and nanoscale structures, where temperature effects and foundational interactions are critical. Furthermore, the fluctuation of waves is somewhat reduced in the examined model.