Response of Generalized Thermoelastic for Free Vibration of a Solid Cylinder with Voids Under a Dual-Phase Lag 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.