M.Ya.Semkiv, G.M.Zrazhevskii, V.T.Matsypura
Diffraction of normal SH-waves on a finite length crack in elastic waveguide

Acoustic bulletin, Vol. 16 1, (2013-2014) p.54-63
The paper deals with considering of propagation of SH-wave in the elastic waveguide with a finite length crack and stress-free boundaries. A diffraction of elastic waves on a crack is analyzed. The method of partial domains is used for solving of the problem, that reduces it to the infinite system of algebraic equations with respect to unknown amplitudes. The obtained system is solved by the modified method of residues of analytical function which is based on calculating of the contour integral as a sum of residues of analytical function in the complex plane. The properties of this function are determined by location of the poles and zeros chosen so that the residue series coincide with the abovementioned system. In doing so, the coefficients at the unknown values in equations may be identified with the residues. Presence of the finite crack gives rise to the additional infinite system of algebraic equations caused by the shift of zeroes of the function. The numerical solution of the problem yields the frequency dependencies of energy transmission and reflection coefficients through the domain containing the finite crack.
an elastic waveguide, normal SH-wave, transmission and reflection coefficients, crack, method of residues