Extension of Surface Variational Principle to Nonsymmetric Acoustic Radiation and Scattering Problems.

This thesis investigates acoustic radiation and scattering from axisymmetric structures (rigid bodies and elastic thin shells of revolution) under arbitrary, harmonic excitation. The technique used to solve these problems is the surface variational principle (SVP). The formulation uses a series of basis functions spanning the entire surface to describe the surface responses, in the manner of analytical type solution. In this thesis, SVP is first extended to slender rigid bodies of revolution under non-axisymmetric excitations, then modified to model scattering from a plane acoustic wave at arbitrary incidence. The wavenumber-based formulation of SVP is developed, which represents the surface response as waves propagating simultaneously in both the azimuthal and meridional directions. Numerical results obtained from SVP for radiation from vibrating rigid bodies and for scattering from stationary rigid bodies are compared to analytic solutions for spheres, and to results obtained from the CHIEF and SHIP boundary element programs for hemi -capped and flat-ended cylinders. The structural dynamics of elastic thin shells are described according to Love's assumptions. Azimuthal dependence is described by Fourier series, while Ritz series are used to represent the meridional dependence of the shell displacement components. The novel feature of the latter is the use of basis functions that are the eigenmodes of a spherical shell mapped onto the meridian of the shell, which assures satisfaction of all continuity conditions at the apexes. By enforcing continuity of normal velocity and pressure on the wetted surface, SVP is joined with Hamilton's principle for the shells to derive a system of algebraic equation governing acoustic radiation and scattering form shells. To test the nonsymmetric features of SVP a submerged spherical loaded by a point force at its equator is compared to an analytic solution. Its accuracy for slender cylinders is tested by comparing SVP and SARA-2D results fur a hemi-capped cylindrical shell subjected to a ring load. For each example, the convergence properties of SVP are examined in detail by viewing both the dependence on series length of series coefficients and of surface distributions. The behavior of SVP in the vicinity of a "forbidden frequency" is studied.