TABLE OF CONTENTS This chapter presents a review of elastic wave propagation in elastic media. SHM methods based on elastic waves propagation are very diverse, and a number of approaches exist. However, a good understanding of SHM wave propagation methods cannot be achieved before a fundamental grasp of the basic principles that lay at the foundation of wave generation and propagation in solid media.
The chapter adopts an incremental step-by-step approach to the description and presentation of the wave propagation problem, which can become quite complicated in some cases. The chapter starts with the discussion of the simplest case of wave propagation the study of the axial waves propagating in a straight bar. This simple physical example is used to develop fundamental principles of wave propagation, such as wave equation and wave speed; d Alembert (generic) solution and separation of variables (harmonic) solution; the contrast between wave speed and particle velocity; acoustic impedance of the medium, and the wave propagation at material interfaces. The concept of standing waves is introduced, and the correspondence between standing waves and structural vibration is established. The power and energy associated with wave propagation in a simple bar are introduced and discussed.
After studying the propagation of simple axial waves in bars, the more complicated problem of flexural wave propagation in beams is introduced and discussed. The equation of motion for flexural waves is derived and discussed. The general solution in terms of propagating and evanescent waves is derived. The dispersive nature of...
