A time-domain energy theorem for the scattering of plane elastic waves (Q1064122)

A time-domain energy theorem for the scattering of plane elastic waves by an obstacle of bounded extent is derived. The obstacle is embedded in a homogeneous, isotropic, perfectly elastic medium. As to the elastodynamic behavior of the obstacle no assumptions have to be made; so, lossy, nonlinear and time-variant behavior is included. As to the wave motion, three different kinds of time behavior are distinguished: (a) transient, (b) periodic, and (c) perpetuating, but with finite mean power flow density. For these cases, the total energy (case (a)) or the time- averaged power (cases (b) and (c)) that is both absorbed and scattered by the obstacle is related to a certain time interaction integral of the incident plane wave (P or S) and the spherical-wave amplitude of the scattered wave of the same type (P or S) in the far-field region, when observed in the direction of propagation of the incident wave.