Study of wave propagation in elastic and thermoelastic solids

Abstract

Lamb wave (1917), which propagate in solid plates with free boundaries, are elastic perturbations for which displacement occurs both in the direction of wave propagation and perpendicular to the plane of plate. These waves are commonly used in ultrasonic non-destructive testing applications. Rayleigh surface waves have been well recognized in the study of seismology, geophysics and geodynamics. These types of surface waves propagate in half space. In the present work, a mathematical analysis has been done to study Rayleigh and Lamb waves in Thermoelastic solids in the context of Generalized theories of Thermoelasticity. The thesis has been divided into four chapters. Chapter 1 includes the discussion of classical theory of elasticity and Generalized Hooke’s law. This chapter also includes a brief theory of Thermoelasticity and Generalized Thermoelasticity. In Chapter 2, we have studied Rayleigh waves in homogeneous isotropic elastic half space and Lamb waves in homogeneous isotropic elastic plate. Formulation of the problem is done and equations are solved by assuming the boundary conditions. Chapter 3 includes the discussion of Generalized Thermoelastic waves in homogeneous isotropic plates. The secular equations are derived and discussed in this chapter. The variations of phase velocity with wave number are shown graphically. Chapter 4 includes the discussion of Rayleigh waves in Generalized Thermoelastic half-space. The secular equations are derived and discussed in this chapter. The variations of phase velocity with wave number are also shown graphically.