Reflection and Transmission of Elastic Waves by a Periodic Array of Cracks

The interaction of elastic waves with a planar array of periodically spaced cracks of equal length is investigated. For normal incidence, reflection and transmission of longitudinal and transverse wave has been considered. Application of finite Fourier transform techniques reduces the solution of the mixed-boundary value problem for a typical strip to that of a singular integral equation. The solution has been obtained numerically. The reflected and transmitted far-field displacements are shown to be superpositions of a finite number of propagating body-wave modes. The numerical results have been checked by an application of the balance of rates of energies. The reflection coefficients have been plotted versus both the frequency and the ratio of crack length to crack spacing. The results according to exact elastodynamic theory have been compared with two approximations. Good agreement is observed at low frequencies.