Time-domain boundary integral equations for 3D problems of elastic wave diffraction on a thin rigid inclusion (Q2754766)

The total displacement field in elastic space is represented as a sum of incident and scattered field; both they satisfy Lamé equations of motion. Boundary conditions on a rigid inclusion reflect its ability to displace and rotate by a small angle. The problem formulation also includes equation of motion of the weighty inclusion and the corresponding initial and boundary conditions. Integral representation of the problem solution is obtained using the Papkovich-Neuber representation in elastodynamics. Wave functions, that enter this representation, are written as wave potentials (integrals) over the domain occupied by inclusion. Then, boundary integral equations and differential equations describing motion of inclusion, which form a full system, are derived. Their solution determine diffracted displacements at any point of elastic medium.