Dynamic analysis of rectangular plates with a single side crack and in contact with water on one side based on the Rayleigh–Ritz method

Abstract

A computational method is proposed based on the Rayleigh–Ritz method for the analysis of dynamic characteristics of a baffled rectangular plate with an arbitrary side crack and in contact with an infinite water domain on one side. Based on the hypothesis that the water is incompressible, inviscid and the motion is irrotational, the added mass density expressed by the displacement trial functions is obtained by means of Green function method. The behavior of crack is described by the corner functions, and the natural frequencies and the corresponding modes are calculated through the Rayleigh–Ritz technique. The validity and the accuracy of the proposed method are demonstrated based on the comparison with the results obtained by ANSYS and those published in other literature, and the influences of water on the natural frequencies and mode shapes of the rectangular plates with side cracks are investigated. It is illustrated that the differences between dry and wet mode shapes increase with increasing mode order on the whole, except for the completely free plates, and the differences are evident for some higher modes.