Abstract The article deals with the estimation of natural frequencies of surface and acoustic waves in fluids using the boundary element method. The phenomena appear in an incompressible or compressible fluid, respectively, and are described by the Laplace or Helmholtz differential equations. The Helmholtz equation fundamental solution contains the wavenumber, which remains unknown under integral operators in the equivalent inverse formulation. The multiple reciprocity method, in which wavenumber-independent higher order fundamental solutions of the Laplace equation occur, overcomes this difficulty. Moreover, this method gives a consistent description in which the incompressible fluid appears as a particular case of the compressible one. This article is divided into two parts: fluid in a rigid and flexible tank. An algorithm allows to take into account couplings between surface and acoustic waves and also tank and included fluid vibrations. The problems related to the interpretation of numerical results are widely discussed in the examples enclosed. The experience gained as a result of the analyses made it possible to compile a number of valuable advices for future research of the discussed problem.
Grzegorz Waśniewski (Thu,) studied this question.