Moore–Gibson–Thompson heat conduction model under the Klein–Gordon (KG) nonlocality for a thermoelastic solid cylinder with voids

This study aims to examine the behavior of thermoelastic vibrations in a
solid cylinder containing voids using a novel approach that involves the
Moore–Gibson–Thompson equation for heat conduction within the context
of Klein–Gordon nonlocality. This unique method offers a fresh perspective
on heat transfer in elastic materials with voids. The results of this study,
which can provide valuable insights for designing structures with better
thermal stability and vibration resistance, were obtained by focusing on
vibrations caused by thermal shock at the cylinder surface. The research
findings can potentially contribute to designing structures with enhanced
thermal stability and resistance to vibrations. In our numerical programming,
we used the Laplace transform technique, which was implemented
in Mathematica software, to analyze the system’s response to thermal
shock. Specifically, we applied Durbin’s Fourier series-based method for
the numerical inversion of the Laplace transform, which has proven efficient
and accurate for this type of problem. Graphical representations were
created from numerical data. Different theoretical approaches were compared
to illustrate how phase lags and nonlocally influence physical phenomena.
These findings indicate that the size of the voids plays a crucial
role, with practical implications for the design and performance of materials.
Additionally, the anisotropy of waves is relatively minor for a cylinder
with voids under the effect of the examined model.