Acoustic harmonic radiation from fluid-loaded spherical shells using elasticity theory

Abstract

The finite Legendre transform technique is used to address the problem of acoustic harmonic radiation from fluid-loaded elastic spherical shells subjected to axisymmetric force excitations. The partial wave series for the response parameters such as the normal velocity of the shell surface, the pressure on the outer surface of the shell, and the far-field pressure are obtained using the mathematical theory of elasticity. Expressions for the input admittance and the transfer admittances for a ring force are also derived. Numerical results are presented for the velocity of the shell, the pressure on the shell, and the far-field pressure directionality patterns as a function of frequency, the relative thickness of the shell, and the location of the force. For low frequencies, the results are compared to those obtained by using a thin shell theory. The convergence properties of the partial wave series as a function of the frequency are also discussed.