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A method for calculating the sound radiation of underwater cylindrical shells in low frequency band by using the equivalent beams is investigated in this paper. The vibrations of cylindrical shells with large length-to-radius ratio L/a>10 are similar to those of beams in very low frequency band, in which underwater sound radiation characteristics of cylindrical shells are mainly dominated by beam-type modes. If the structural parameters and boundary conditions of a beam model are same as those of a cylindrical shell, the radiated sound power levels will be correspondence in low frequency band. However, One-dimensional beam theoretical model only considers about the transverse displacement, the coupling effects of displacements in other directions are neglected. 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, in which different Young's modulus values of the equivalent beam model are searched to make the beam-type modal frequencies identical to those obtained by cylindrical shell theoretical model. For convenience, the interaction between the structures and water is approximated to added mass. The results show that the equivalent Young's modulus values are mainly dominated by the length-to-radius ratio for cylindrical shells, and the effect of the shell thickness on those can be neglected. The efficient and accurate numerical solutions are presented to validate the proposed method.

Based on wave superposition method (WSM), radiated noise can be predicted quickly by monitoring the vibration data on machine surface. However, this method may produce great error for complex vibration distribution. The main cause is the improper configuration of equivalent sources. In order to solve this problem, an equivalent source configuration based on the least mean square method (LMS) is put forward for typical structure in this paper, in which a few reference points of sound field pressure should be measured ahead to search the optimal equivalent source position automatically. Since the structure has been equivalent to an array of monopole sources by WSM, the prediction for mechanical noise with boundaries can be realized by changing Green function. The result shows that the radiated noise of structure, for different excitations, can be predicted precisely from the surface velocity by WSM once the optimal equivalent source position is determined by LMS using the reference points of sound pressure field.