A MATHEMATICAL MODEL FOR THE QUADRUPOLAR OSCILLATIONS OF THE BRAZILIAN GRAVITATIONAL WAVE DETECTOR

摘要

In this work we present results relative to a mathematical model for the mechanical response of the Brazilian Mario SCHENBERG gravitational wave (GW) detector to such waves. We found the physical parameters that are involved in this response assuming a linear elastic theory. Adopting this approach we determined the system’s resonant frequencies for the case when six i-mode mechanical resonators are coupled to the antenna surface according to the arrangement suggested by Johnson and Merkowitz: the truncated icosahedron configuration. This configuration presents special symmetries that allow for the derivation of an analytic expression for the mode channels, which can be experimentally monitored and which are directly related to the tensorial components of the GW. Using this model we simulated how the system behaves under a gravitational sinewave quadrupolar force and found the relative amplitudes that result from this excitation.