On Some Mathematical Developments and Implications of Generalized Thermoelasticity

Abstract

In this thesis, the fundamental concepts of elasticity and thermoelasticity are discussed. The transition from classical thermoelasticity to generalized thermoelasticity has been described. A brief discussion about some well established models of generalized thermoelasticity theory has been made. Basic concept of memory dependent derivative and its properties are presented. The main objective of this thesis is to further the study of various applications of generalized thermoelasticity theories. By taking temperature dependent material moduli into consideration, the investigations have been done in the context of generalized thermoelasticity theories. The memory responses on stress and temperature fields in an isotropic magneto-thermoelastic medium and effects of temperature dependent material moduli with energy dissipation in a magneto-thermoelastic medium have been investigated. Thermoelastic analysis of a medium under mechanical strip load with laser pulse heat source has been made in the context of an advanced thermoelasticity model involving higher order memory dependent derivatives with dual time delay factors. The nature of physical quantities of a medium in presence of laser pulse heat source has been investigated in the context of three phase lag model of generalized thermoelasticity theory. The analytical solutions for the field variables are obtained in Laplace-Fourier transformed domain. To depict the solutions in physical domain in various cases, discretized numerical inversion techniques are utilized. newline A problem of Rayleigh wave propagation in a transversely isotropic elastic half-space overlaid by a transversely isotropic elastic layer has also been investigated. The layer and half-space are considered to be perfectly bonded. The investigations are made in the context of Lord-Shulman theory of generalized thermoelasticity. Numerical computations are made to analyze nature of various quantities in different cases. newline newline