Symbolic computation aids for SAW and BAW analysis

One objective of symbolic computation is to obtain solutions to problems as explicit analytical or symbolic expressions, thereby eliminating time-consuming iterative search algorithms. Another objective is to carry out various mathematical operations which are currently only possible numerically. In the study of surface-acoustic-wave (SAW) propagation and waveguiding the linear system is described by transmission matrices with ranks ranging from 4 to 8, depending on material anisotropy and crystalline orientations. In the study of bulk-acoustic-waves (BAWs) the systems have rank ranging up to 4. It is shown how symbolic computation software is used to obtain analytical results (some previously known, some new) for some very simple BAW and SAW problems. As one example, the Rayleigh wave problem on an isotropic half-space is used to show how DERIVE and MAPLE are exploited to develop an explicit formula for the Rayleigh wave velocity for an arbitrary material