Wave propagation in elastic waveguides with a finite length crack

In the presented work the propagation of SH-wave in elastic waveguides with finite length cracks in the case of free boundaries is considered. The complete analysis of diffraction of elastic waves on cracks of finite length is performed. This problem was solved by the method of partial regions. Matching procedure reduce to the infinite system of algebraic equations for unknown amplitudes. This system is solved by the use of method of residues of analytical functions. Residues method is based on calculating of integral as the sums of residues of analytical function f(w) in the complex plane. A finite crack in elastic waveguides makes it necessary to solve additional infinite system of algebraic equations caused by shift of zeroes of functions f(w). Shift zeroes of function are solutions of an additional system. A displacement components of diffraction fields is obtained. The exact analytical solution on the base of the analytical functions methods is built. The reflection coefficient (the ratio of power flux incident wave to the power flux reflected wave) as well as transmission coefficient are calculated. All of that was obtained for different wavelengths of incident wave. Number of members in the infinity products, which are includes in defined amplitudes, to ensure energy conversation law is defined.