Wave evolution, reflection, and transmission along inhomogeneous waveguides

One-dimensional wave propagation along an inhomogeneous waveguide, such as an acoustic horn, a plate strip, a rod, or a beam is considered. The equati ons of motion of a generic waveguide are written in first order form, and t he properties of the (position-dependent) eigenvalues and eigenvectors of t he system are deduced by considering the symmetry and/or the energetics of the system. The equations of motion are then transformed to "wave co-ordina tes" based on the right eigenvectors of the system, and a perturbation meth od is employed to study wave propagation along deterministic, periodic, and random waveguides. Attention is then turned to wave reflection at a "cut-o ff' cross-section, and a general result for the phase of the reflection coe fficient is derived. The general theory is illustrated by application to ro d and beam examples. The method can be likened to a "coupled modes" approac h in which the properties of the eigenvectors (or "'modes") arising from sy mmetry and/or energetics are exploited. (C) 1999 Academic Press.