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

Based upon the modal analysis by FEM, some relevant parameters of every element on a clamped thin circular plate with an artificial radial crack are extracted. After the Rayleigh's integral is discretized, the axial pressure distribution and the distribution of the sound field on the spherical surface r = 0.5 m radiated by the crack plate are computed. It is shown that the radial crack doesn't only make the modes split into symmetrical and antisymmetrical modes about the crack except the first mode, but also changes the distribution of the sound field obviously. The validation of the method is illustrated by the sound field radiated by the intact circular plate, and it is suitable for computing sound field radiated by a circular plate with different kind of through crack. Moreover a simple computational method for the vibration frequencies of a circular clamped baffled plate with an artificial crack in water is described. Under the conditions that the plate vibrates in small amplitude and the modal deflection in water equals that in vacuo, the added mass density due to the water pressure is expressed using Rayleigh's integral. Then the relationship among vibration frequency of the plate in water and that in vacuo and the Nondimensionalized Added Virtual Mass Incremental (NAVMI) is obtain 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 singular dot, the value of NAVMI is obtained by discretizing the integral. Moreover the vibration frequencies of the plate are computed using iterative method, which begins with the in vacuo eigenfrequency and continues until in-water eigenfrequency converges. The present approach is validated by comparison the NAVMI computed here with the results of Reference Kwak M K. J. Sound Vib., 1997; 201 (3): 293-303.