Waves in Fluids and Solid Structures

To understand the process of acoustic interaction between solid structures and fluids, it is essential to appreciate the wave nature of responses of both media to time-dependent disturbances from equilibrium, whether these are transient or continuous. This chapter gives an introduction to the general mathematical description of unidirectional harmonic wave motion. Various forms and characteristics of the principal types of wave that are important in vibroacoustics are discussed in the chapter, along with their behaviors in a number of archetypal forms of structure. The chapter introduces the unified mathematical description of temporal and spatial distributions of wavefield variables and illustrates the forms of vibrational waves that travel in various ideal forms of structure, such as uniform beams, flat plates, and thin-walled, circular cylindrical shells. The phenomenon of wave dispersion that relates wave speed and frequency form the basis to categorize regimes of wave interaction at interfaces between different media and different forms of structure. The phenomena of natural frequencies and modes of bounded elastic systems and the related phenomenon of resonance are illustrated and explained in the chapter in terms of wave reflection and interference. The chapter provides a brief overview to probabilistic modeling of natural frequency distributions and related quantities that are employed in statistical energy analysis.