Vibration analysis of thermoelastic micro-beams on a Pasternak foundation with two parameters using the Moore–Gibson–Thompson heat conduction model

This study investigated the thermoelastic vibration behavior of microbeams supported by a Pasternak foundation, characterized by two elastic parameters: the shear layer modulus and the Winkler modulus.
The thermoelastic behavior of the beam was modeled using the Moore–Gibson–Thompson (MGT) heat conduction theory, which accounted for finite thermal wave speeds and included a higher-order time derivative to
effectively address heat conduction dynamics in small-scale structures. The governing equations were derived
from the coupled theories of generalized thermoelasticity and beam mechanics, integrating the effects of the
foundation. The research examined how foundation parameters, thermal relaxation times, and beam geometry
influenced vibration frequency, thermal damping, and the stability of the microbeam. Numerical simulations
were performed to demonstrate the effects of material properties, foundation stiffness, and thermal loading on
the dynamic behavior of the microbeam. The findings offered valuable insights for the design and optimization
of microbeams in advanced engineering applications, such as MEMS devices and nanoscale structures, where
thermal effects and foundation interactions were crucial.