A unified semi-analytic method for vibro-acoustic analysis of submerged shells of revolution

Abstract

A unified semi-analytic method is developed to predict vibro-acoustic responses of submerged shells of revolution. The shell is firstly decomposed to several narrow shell segments to be treated as conical shells. By employing Flügge shell theory and power series, displacements and forces at any cross-section of conical shells are expressed as eight unknown coefficients. Then, expanding surface pressure and velocity as Fourier series in circumferential direction, the surface Helmholtz integral equation is reduced to the line integral along the generator line, and the pressure is further represented as displacements of all segments through meshing the generator line to some 3-node isoparametric elements and utilizing relationships of velocities and displacements. Last, continuity conditions between adjacent segments, which include modifications introduced by acoustic pressure, and elastic boundary conditions are assembled to the finial vibro-acoustic governing equation of submerged shells of revolution. Through comparing vibro-acoustic results of present method with ones in appropriate references or calculated by FEM/BEM for independent conical, cylindrical and spherical shells and combined spherical-cylindrical-spherical and conical-cylindrical-spherical shells, rapid convergence, wide application and high accuracy of the semi-analytic model are demonstrated. Meanwhile, contributions of different circumferential modes and different compartments of the combined conical-cylindrical-spherical shell to vibro-acoustic responses are investigated.