A method for predicting the vibrations of underwater cylindrical shells by using the equivalent beam model

Abstract

The vibrations of cylindrical shells with large length-to-radius radio are similar to those of beams in very low frequency band. One-dimensional beam theoretical model is only considered about the transverse displacement, neglecting the coupling effects of displacements in other directions. Only the first order beam-type modal frequency, not the other higher orders, of cylindrical shells can be predicted precisely by one-dimensional beam theoretical model. To solve this problem, an equivalent beam theoretical model is established, based on Euler-Bernoulli beam theory, in this paper. In this model, a cylindrical shell model is considered as a beam model with the same structural parameters and boundary conditions, the interaction between the structures and water is approximated to added mass. Different Young's modulus values have been searched to make the calculated results identical to those obtained by cylindrical shell theoretical model. The results show that the beam-type modal frequencies are mainly dominated by the length-to-radius radio for shells with length-to-radius radio L/a>10 and radius-to-thickness radio a/h>20, and the effect of the shell thickness to the modal frequencies can be neglected in such conditions. The equivalent Young's modulus curves for the first five order beam-type modal frequencies of cylindrical shells with different length-to-radius radio have been calculated.