SCATTERING OF A FLEXURAL WAVE BY A FINITE STRAIGHT CRACK IN AN ELASTIC PLATE

The diffraction of flexural waves by a short straight crack in an elas tic thin plate is considered. The vibrations of the plate are describe d by the Kirchhoff model. The Fourier method transforms the problem to integral equations of convolution on an interval. The theorems of exi stence and uniqueness of solutions for these equations are proved. The numerical procedure is based on the orthogonal polynomials decomposit ion method. It leads to infinite systems of algebraic equations for th e coefficients. The truncation method is proved to be applicable to th ese systems due to the special choice of the polynomials. A physical i nterpretation of numerical and asymptotic results obtained for the dir ectivity of the scattered wave and for the stress intensity coefficien ts near the ends of the crack is suggested.