Introduction

Wave–mode duality concepts were introduced and discussed in some detail in chapter 1. It was pointed out that, whilst the lumped-parameter approach to mechanical vibrations is adequate to describe mode shapes and natural frequencies, it is not suitable for relating vibrations to radiated noise. One therefore has to use the fundamental wave approach to obtain an understanding of the essential features of mechanical vibrations as they relate to sound radiation and sound transmission. These interactions between sound waves and the mechanical vibrations of solid structures form a very important part of engineering noise and vibration control.

Because solids can store energy in shear and compression, all types of waves can be sustained in structures – i.e. compressional (longitudinal) waves, flexural (transverse or bending) waves, shear waves and torsional waves. On the other hand, since fluids can only store energy in compression, they can only sustain compressional (longitudinal) waves. For reasons which will become evident later on in this chapter, flexural (bending) waves are the only type of structural wave that plays a direct part in sound radiation and transmission. At this stage it is sufficient to note that the primary reason for this is that the bending wave particle velocities are perpendicular to the direction of wave propagation (see Figure 1.1b) resulting in an effective exchange of energy between the structure and the fluid.