The condition for beam-bending modes to dominate in the vibro-acoustic behavior of a circular cylindrical shell

Abstract

The acoustic radiation from circular cylindrical shells is of fundamental and applied interest primarily because cylindrical shells are widely used in industries. However, according to previous studies, only a few special cases, for example, a cylindrical shell under the assumption of beam bending, can be solved analytically. Obviously, in practice, the vibration behavior of a cylindrical shell may not be assumed to be beam bending in the whole frequency range of interest. This is because the vibration behavior of a cylindrical shell changes with frequency. Therefore, it is important to determine the condition under which a circular cylindrical shell would behave like beam bending so that the analytical solution could be used correctly. In this paper, an analysis of the basic vibration behavior of circular cylindrical shells using the Love’s equations shows that for an infinite length cylindrical shell, the beam-bending wave would always be propagating with other flexural waves of different circumferential mode numbers. However, for a finite-length circular cylindrical shell, below the cutoff frequency of n=2 mode, beam-bending modes would dominate the vibration response so that it can be treated as a beam with reasonable accuracy. This analytical result is supported by calculations obtained using the boundary element method.