Fractional Moore–Gibson–Thompson Heat Conduction for Vibration Analysis of Non-Local Thermoelastic Micro-Beams on a Viscoelastic Pasternak Foundation

This study aims to investigate the behavior of viscoelastic materials exhibiting
complex mechanical behavior characterized by both elastic and viscous properties. They
are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and
earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial
for predicting its performance under dynamic loading conditions. In this study, we modify
the equations governing the thermoelastic resistance to describe the thermal variables of a
thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation
by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality.
The temperature, bending displacement, and moment were computed and graphically
displayed using the Laplace transform method. Different theoretical approaches have been
compared in order to explain how the phase delay affects physical phenomena. Numerical
results show that the wave fluctuations of variables in thermoelastic micro-beams are
slightly smaller for the studied model and that the speed of these plane waves depends on
fractional and non-local parameters.