Nonlocal Dynamics in Porous Thermoelastic Plates: A New Framework for Multi-Phase-Lag Theory and Microtemperature Effects

This paper establishes a fresh mathematical framework for the investigation of improved multi-phase-lag theory for porous thermoelastic plates with microtemperature under nonlocal parameters. This model is made simpler by dimensionless quantities, and the governing equations are solved using normal mode analysis. For stress-free plate boundaries, the frequency equations for symmetric and skew-symmetric modes of propagation are established. The effects of dual-phase-lag and nonlocal parameters on the phase velocity and attenuation coefficient versus wave number for both symmetric and skew-symmetric modes are plotted for stress-free thermally insulated plate boundaries. Additionally, for the Lord-Shulman (L-S), Green–Naghdi Type II [G-N(II)], and refined multi-phase-lag theories, graphical visualizations of the phase velocity and attenuation coefficient are provided. The mathematical model presented in this study is an essential and imperative instrument for examining a wide range of problems associated with scientific research, product, process, and industrial development.