Chapter 2 - Elastic Waves in a Perfect Elastic Solid

Abstract

Wave motion has been discussed in the previous chapter, and the acoustic wave equation for describing general wave motion has been derived. In this chapter, we will discuss elastic wave propagation in solids based on continuum mechanics. The acoustic wave equation is suitable for wave propagation in seawater but is not accurate in solid media that have tangential traction ability. In this chapter, we will discuss elastic waves propagated in a perfectly elastic solid based on the theory of continuum mechanics. Continuous media are composed of many fully connected grains, such as different minerals; the product of the volume of a grain and its density is called the mass element. Forces are classified as surface force and body force, and we must use different expressions to show these forces. Surface force and body force should not be confused. Continuum mechanics starts from continuous media and continuous Eqn (1.2). Wave propagation in continuous media deals with mass grains and their surfaces, but not with free-motion particles in vibration.