Introduction to Elastic Wave Propagation

This text presents the basic concepts and methods of the theory of wave propagation in elastic materials. The linear theory of elasticity is presented, culminating in the displacement equations of motion. One-dimensional waves are analyzed through the D'Alembert solution and the method of characteristics. Examples of harmonic waves include reflections of plane waves at interfaces, Rayleigh waves, waves in elastic layers, and waves in layered materials. Transient waves are discussed in the context of integral transforms, including introduction to fast Fourier transform methods and the Cagniard-de-Hoop technique. Analytical methods in nonlinear wave propagation are presented, including techniques based on characteristics and the analysis of shock and acceleration waves through singular surface theory.