Response of an Interferometer Mounted on an Elastic Square Plate to Gravitational Waves

Laser-interferometric gravitational wave detectors are commonly modeled as being at rest in transverse-traceless coordinates (and thus geodesic). In this paper, we analyze what happens if the interferometer is mounted on a material that can undergo elastic oscillations caused by the gravitational wave. We thus compute the response of a two-dimensional elastic material to linearized gravitational radiation and compute the resulting response of a laser interferometer, mounted on such a plate.