Scattering of flexural waves from a hole in a thin plate with an internal beam

The scattering of flexural waves by a hole in a thin plate traversed by a beam is modeled here by coupling the Kirchhoff-Love and the Euler-Bernoulli theories. A closed form expression is obtained for the transfer matrix (T-matrix) relating the incident wave to the scattered cylindrical waves. For this purpose, a general method has been developed, based on an analogous impedance method for acoustic waves, for calculating the T-matrix for flexural wave scattering problems. The T-matrix for the problem considered displays a simple structure, composed of distinct sub-matrices which decouple the inside and the outside fields. The conservation of energy principle and numerical comparisons with a commercial finite element simulator have been used to prove the theory.