Interaction between elastic longitudinal shear waves and radially distributed cracks (Q2714556)

An elastic medium is considered under the conditions of antiplane deformation with \(N\) cracks occupying the segments \(\,\theta=\theta_l\), \(\,r\in[a_l,b_l]\), \(\,l=1,2,\dots,N\,\) in the plane \(\,(r,\theta)r>0\), \(\,-\pi<\theta<\pi\). The cracks are affected by the longitudinal shear wave propagating in the medium and causing the transpositions NEWLINE\[NEWLINE w_0(r,\theta_l) = A\,\exp@,(ik_2r\,\cos@,(\theta-\theta_0)),\quad\,\, k_2^2 = \frac{\rho\omega^2}{G}, NEWLINE\]NEWLINE where \(\,\rho\) is the medium density, \(G\) is the shear modulus and \(\omega\) is the oscillation frequency.\flushpar The author applies the discontinuous solutions to the Helmholtz equation. This allows an efficient investigation of the peculiarities of the appearing dynamical stress state.