An Analytical Solution for Free Flexural Vibration of a Thin Cylindrical Shell Submerged in Acoustic Half-Space Bounded by a Free Surface

An analytical solution is proposed for the free flexural vibration of a finite cylindrical shell submerged in half-space bounded by a free surface in the low frequency range. The motion of the shell is described by the Flügge shell theory and the fluid surrounding the shell is assumed to be an acoustic media. The free surface effect is considered by satisfying the pressure release boundary condition. The accuracy of the present method is verified through comparison with the finite element solution. To throw light on the influence mechanism of free surface on the coupled modal frequencies, a modal added mass is introduced and calculated. Numerical results show that when the shell is close to the free surface, the presence of free surface will make a negative contribution to the modal added mass and finally result in the corresponding increase of the coupled modal frequencies. But the free surface effect will decrease when the immersion depth of the cylindrical shell increases. Finally, the free surface effect can be neglected if the immersion depth is higher than four times the shell radius. This conclusion is helpful to select proper test environment for an experiment on the dynamic characteristics of submerged cylindrical shells.