Effects Of A Crack And Water On The Characters Of The Vibration And The Sound Field Radiated By A Thin Plate

A thin plate is an essential element comprising a mechanical structure andis extensively utilized on transportation tools such as an aeroplane, a ship etc.. If a crack emerged on a plate element of these bodies and weren't found out in time, accidents such as fluid leakage, structure rupture and transportation mishap would be brought about. Therefore testing of a crack in a structure, particularly on a plate has been becoming an important research topic. There are various kinds of methods for testing a crack on a plate, among which testing sound from a plate excited by a beat is an ancient method. In this method it is very difficult to accurately compute the sound field radiated by a cracked plate because of troublesome expression of the deflection. The vibration characters of a cracked plate have been investigated only for simply-supported boundary condition, but for other boundary conditions, the vibration and sound field of a cracked plate are seldom studied. Moreover the vibration and the sound field of a structure in water such as a submarine are also an attractive problem. Water effects the vibration of a plate element on the crust of the body, and if there is a crack on it, the crack also effects the vibration and the sound field from the plate. Under several approximate conditions the vibration frequencies of an intact plate in water are investigated by using the Rayleigh-Ritz method, disturbance method etc.. These methods are suitable only for specific boundary conditions and specific shape of a plate, and do not involve a crack in a plate.Based upon fathers' work and expressing the deflection as the summation of orthogonal polynomials, the vibration frequencies and the deflections of a cantilever square plate with a crack perpendicular to the clamped edge, a circular clamped plate with a radial crack or an arc crack, and an intact cantilever square plate and a circular plate are solved by the Rayleigh-Ritz method with a sub-sectioning techniques and the Rayleigh-Ritz method, respectively for the first time. Then the characters of the sound field distribution are computed. As for a thin plate with a complex crack (a cross crack or a slanting crack), after modal analysis is carried out by finite element method andsome relative data are extracted, the distribution of the sound field radiated by the cracked plate is obtained by discretizing the Rayleigh's integral. The effect of the length, the shape, and the location of a crack on the vibration frequencies and the directivity patterns of the sound field radiated from the plate are investigated. The validation of the method is illustrated by comparing the solution to the sound field radiated by the intact plate obtained here with that obtained by another method. Experimentally the modal frequencies of the cracked plate are determined by analysing the spectra of the sound field radiated from the plate excited by a beat. The experimental results are in agreement with theoretical results. In addition, the effects of the length, the width, the depth and the location of a non-through crack on the vibration frequencies of a thin plate are investigated.A simple method for computing the modal vibration frequencies and sound radiation efficiencies of a thin cracked baffled plate 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 the 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 the 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 point, the value of NAVMI is obtained by discretizing the integral. Moreover the modal vibration frequencies and sound radiation efficiencies of the p...