Analytical and experimental study of the vibro-acoustic behavior of a semi-submerged finite cylindrical shell

Abstract

The vibro-acoustic behavior of a semi-submerged finite cylindrical shell is studied theoretically and experimentally. An analytical form of the vibro-acoustic coupling equation is developed using the wavenumber transformation and separation of variables for the sound pressure and the mode expansion for the shell's motion. The far-field radiation sound pressure is derived by utilizing the stationary-phase approximation. The radial velocity, radiated sound power, and sound pressure directivities (including the circumferential and axial directivities) from analytical models are compared with numerical and experimental results to verify the method. The assumption that the shell is terminated by semi-infinite rigid baffles is the main reason for the deviations between the analytical and experimental results. Below the ring frequency, acoustic radiation from a semi-submerged finite cylindrical shell occurs primarily because the air–liquid demarcation points on the shell surface act as radiation sources. Therefore, the circumferential and axial directivity patterns of a semi-submerged finite cylindrical shell can be approximated as a superposition of two in-phase dipoles formed by the air–liquid demarcation points and as a superposition of two in-phase dipole line sources, respectively. Simple formulas are derived to predict the circumferential and axial directivity patterns. This is a new and simplified approach for predicting the directivity patterns of a semi-submerged finite cylindrical shell. The vibro-acoustic behavior of a semi-submerged finite cylindrical shell differs from that of a submerged shell, especially the circumferential directivity pattern due to the reflection from the free surface.