A Galerkin Method for Linear Pde Systems in Circular Geometries with Structural Acoustic Applications

A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic and structural acoustic applications. Depending upon the application under consideration, piecewise ,plines or Legendre polynomials are used when approximating the system dynamics with modifications included to incorporate the analytic solution decay near the coordinate singularity. This provides an efficient method which retains its accuracy throughout the circular domain without degradation at the singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coefficients, transform methods for the problems are not investigated. While the specific method is developed for the 2-D wave equation on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the flexibility of the method when approximating the dynamics of more complex systems. 'This research was supported in part by the National Aeronautics and Space Administration under NASA Contract Number NASI-19480 while the author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. Additional support was also provided in part under NASA grant NAG-1-1600.