A note on the motion of a rigid circular particle buried in an elastic solid

The motion of a rigid circular particle buried in an elastic solid is discussed based on the 2D elastodynamic theory. An incident time-harmonic P-wave induces the simple horizontal vibration along the propagation line of the incident wave, and an incident SV-wave also does the simple vibration vertical to the propagation line. Moreover, the incident SV-wave produces the rotational vibration with respect to the center of the particle. Amplitudes of these vibrations are obtained exactly, and their numerical examples show that the amplitudes take a peak/maximum only when the mass density of the particle is larger than that of the surrounding elastic solid. Lastly, the combined incident P and SV-waves produce the particle motion on a retrograde elliptic orbit.