Effects of a crack and water on the characters of vibration and sound field radiated by a circular plate

摘要

Based upon FEM, some relevant parameters of a clamped thin circular plate with an artificial crack are extracted. The axial pressure distribution and the directivity pattern of the sound field on the spherical surface of radius r = 0.5 m radiated by the cracked plate are computed. A simple computational method for the modal vibration frequencies and sound radiation efficiencies of a circular clamped baffled plate with an artificial crack in water is described. Under the conditions that water is incompressible, inviscid and irrotational, and the plate vibrates in small amplitude and the modal deflection in water is equal to that in vacuo, the added mass density due to the water pressure is expressed using Rayleigh's integral. Then the relationship among modal vibration frequency of the plate in water and that in vacuo and the nondimensionalized added virtual mass incremental (NAVMI) is obtained by utilizing Rayleigh method. Based upon the data of modal analysis for the plate in vacuo by finite element method (FEM) and properly dealing with the integral at a singular point, the value of NAVMI is obtained by discretizing the integral. Moreover the modal frequencies and sound radiation efficiencies of the plate are computed using an iterative method. The presented approach is validated by comparing the NAVMI computed here with the results of reference [1]. This method is suitable for computation for vibration model frequency and model radiation efficiency of a baffled thin plate of arbitrary shape in water with a through crack of arbitrary shape.