Scattering of bending waves by open and closed cracks and joints in a fluid-loaded elastic plate

Abstract

An analysis is made of the scattering of bending waves on a thin, fluid-loaded elastic plate by open and closed rectilinear cracks and joints. The scattered field includes transmitted and reflected waves on either side of the crack or joint, together with sound radiated into the fluid. The system is equivalent to two coplanar, semi-infinite plates whose edges meet at the crack or joint. The crack/joint is closed when the gap between the edges is small enough for there to be no flux of fluid from one side of the plate to the other (it being assumed that the free edges of a crack can vibrate without contact). An open crack/joint behaves as a monopole source when the flux is non-zero. For an open crack at frequenciesωbelow the coincidence frequencyωcof the plate, it is predicted that the intensity of the sound generated by the monopole is significantly larger than that scattered when the crack is closed. In the case of a crack in a steel plate in water the difference can exceed 10 dB atω≈ 0.3ωc, and increases rapidly asωdecreases. The acoustic efficiency of a joint at which the flexural motion of the plate is inhibited (by clamping or rib-stiffening, for example) is not significantly altered when the joint is open; small reductions are predicted at low frequencies for a joint in a steel plate in water.