Overview

This chapter will extend the results from Chapter 10 by using more advanced analytical methods for calculating acoustical quantities such as mutual radiation impedance. Before fast computers were available some of the results obtained by analytical methods had limited usefulness when they were expressed as slowly converging infinite series or integrals that required numerical evaluation. Now such series and integrals can be evaluated more easily. In some cases the analytical methods give more physical insight, or can be reduced to a simpler form, than the strictly numerical methods. In this chapter, we will give results for several useful cases obtained by anaylytical methods, along with numerical evaluations. However, the most advanced analytical methods cannot handle the geometries presented by practical transducers and arrays; in those cases finite element numerical methods are necessary.

The influence of fast computing increased rapidly from about 1960 when new numerical methods for calculating sound fields began to be developed, methods which have now grown into the large field called boundary element methods (BEM). These numerical methods, when combined with structural finite element analysis, have advanced to the point where it is feasible to include many structural details of a transducer or an array of transducers as well as the acoustics in the surrounding medium. An example of such calculated results for an array of sixteen transducers, including the water loading, was given in Section 5.6. A brief description of some of these numerical methods will be included in this chapter. It is fortunate...