EXACT BOUNDARY-CONDITION PERTURBATION FOR EIGENSOLUTIONS OF THE WAVE-EQUATION

A perturbation method is presented to analytically calculate eigensolu tions of the two-dimensional wave equation when asymmetric perturbatio ns are present in the boundary conditions. The unique feature of the m ethod is that the sequence of boundary value problems governing the ei gensolution perturbations are solved exactly through fifth order pertu rbation. Two classes of asymmetry are considered: irregular domain sha pes that cannot be treated by analytical means, and variation of the b oundary conditions along the boundary. The unperturbed eigensolutions are those for an annular domain with axisymmetric boundary conditions. Irregularly shaped domains are studied in detail to demonstrate the m ethod and the accuracy of the results, which are compared with exact v alues for the elliptical and rectangular domain cases. The results sho w excellent agreement with these known solutions for large shape disto rtions, an achievement resulting from the extension to higher order pe rturbation. Fourier representation of the boundary asymmetries allows analysis of arbitrary distributions of asymmetry. Additionally, the ex act perturbation solution retains the explicit parameter dependence of continuous system analysis, generates simple expressions for the pert urbed eigensolutions, addresses all distinct and degenerate axisymmetr ic system eigensolutions, and requires minimal computation and program ming. (C) 1998 Academic Press Limited.