Response of General Vibrations for the Thermoelastic cylinder with voids, and Dual-Phase-lage model

This study uses the dual-phase lag model to investigate the behavior of thermoelastic vibrations in a solid cylinder containing
voids, examining the impact of generalized thermoelasticity. This model provides a comprehensive thermoelastic framework
that incorporates time delays between heat flow, temperature change, deformation, and stress. 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. 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 to be 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 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.