Analysis of Nonlinear Acoustic Vibrations of an Axially Moving Submerged Double-Walled Cylindrical Shell

Abstract

In this study, the nonlinear vibro-acoustic dynamics and stability of double-walled axially moving cylindrical shell are investigated. The external surface of the outer shell is in contact with fluid and subjected to oblique incident plane sound wave. Donnell’s nonlinear shallow shell theory is used to derive the nonlinear partial differential equation of the shells for the radial motion. The Galerkin method is employed to discretize the equations of motion into the set of coupled nonlinear non-homogeneous ordinary second-order differential equations. Considering both driven and companion modes, multiple scales method is used to obtain the response of the system. The effects of the ratio of the external to internal shell radius, sound level, incident angle and axial velocity on the frequency response of the system are studied. The results show that, depending on the selection of the system parameters, the effect of driven and companion modes on the frequency response and transmission loss of the system changes.