Modeling of memory-dependent derivative in a fiber-reinforced plate under gravitational effect

ABSTRACT

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a fiber-reinforced thick plate due to the gravitational effects having a heat source, in the context of three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. The upper surface of the plate is free of traction having a prescribed surface temperature while the lower surface rests in a rigid foundation and is thermally insulated. Employing Laplace and Fourier transforms as tools, the problem has been solved analytically in the transformed domain. The inversion of the Fourier transform is carried out using suitable numerical techniques while the numerical inversion of Laplace transform is done incorporating a method on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Excellent predictive capability is demonstrated due to the presence of memory dependent derivative, reinforcement and gravitational effect.

KEYWORDS:

• Caputo derivative
• fiber-reinforced composite
• gravity
• memory dependent derivative
• spatially varying heat source
• three-phase-lag thermoelastic model

Acknowledgments

We are grateful to Prof. S. C. Bose of the Department of Applied Mathematics, University of Calcutta for his valuable suggestions and guidance in preparation of the article. We also express our sincere thanks to the reviewers for their valuable suggestions for the improvement of the article.