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.