State Space Approach to Moore-Gibson-Thompson Generalized Piezo-Thermoelasticity with Memory-Dependent Derivative

Document Type : Research Article

Authors

1 Department of Mathematics and Statistics, Aliah University, Kolkata-700160, India

2 Government General Degree College, Tehatta, Nadia- 741160, India

3 Chengail High Madrasah, Uluberia, Howrah-711408, India

Abstract

The aim of this research is to investigate the thermal and mechanical responses in an isotropic piezo-thermoelastic semi-infinite medium that is subjected to a moving heat source. The exploration has been carried out in the context of two-temperature Moore-Gibson-Thomson generalized thermoelasticity with memory-dependent derivative (MDD). The two-temperature approach is adopted to discern the separate evolution of temperature gradients, while a memory-dependent derivative is employed to capture the historical behavior of the material. The resulting system of partial differential equations is systematically solved in the transformed domain of Laplace using the state space approach, an advanced mathematical technique. The Fourier series expansion technique for numerical Laplace inversion is used to derive the solution for various thermophysical quantities in the real space-time domain. Parametric studies are conducted to explore the influence of the heat source speed and the parameter related to the memory-dependent derivative on the material’s response. The outcomes of this work are presented graphically for a better understanding of the impacts of the parameters considered. Applications of this work extend to diverse areas, including material science, structural engineering, and thermal management systems.

Keywords

Main Subjects

References

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Mechanics of Advanced Composite Structures
Volume 13, Issue 2 - Serial Number 28
In Progress
November 2026
Pages 451-463

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