Study of six mechanical impedance matchers on a spherical gravitational wave detector

Abstract

A spherical gravitational wave (GW) detector has a heavy ball-shaped mass which vibrates when a GW passes through it. Such motion is monitored by transducers and the respective electronic signal is digitally analyzed. One of such detectors, SCHENBERG, will have resonant frequencies around 3.2 kHz with a bandwidth near 200 Hz. The frequencies of other resonant-mass detectors typically lay below 1 kHz, making the transducer development for this higher frequency detector somewhat more complex. In this work we present a series of finite element studies of a sphere coupled to resonant mushroom shaped resonators that will work as mechanical impedance matchers between the sphere and the transducer. We describe the search for a shape of the impedance matcher that might improve the performance of the detector. We find that the normal modes of the coupled system are not exactly degenerate, while theoretical calculations predict that they should be.