When a structure experiences a localized disturbance over a short period of time, an impulse, the energy propagates throughout the structure as waves. When the structure is relatively large so that the waves do not have many interactions with the boundaries (within the observation time), then the behavior is amenable to wave analysis methods; that is, there is a definite space/time relationship for the location of the energy. On the other hand, when the structure is relatively small so that there are many wave reflections, then the behavior is dominated by the vibration characteristics and therefore amenable to spectral and modal analysis methods, as discussed earlier.

Waves can propagate in extended media; common examples are surface water waves and sound pressure waves. They can also propagate in slender members with traction-free lateral boundary conditions; simple examples are rods and beams. Section 7.2 developed spectral analysis tools for these types of members, and therefore we mostly concentrate our wave analysis on these slender members – only briefly do we consider waves in extended media. In a wave context, the slender members are referred to as waveguides.

Introduction to Wave Propagation

This section gives a general introduction to the area of stress-wave propagation. The intent is to establish some of the characteristics of waves that differentiate them from other dynamic behaviors such as vibration. The main idea developed is the distinction between dispersive and nondispersive waves.