2003/12/05 by César A. Costa, Odylio D. Aguiar, Costa, César A. +3
Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0312035
11 pages, 14 figures, submitted to PRD
arxiv created 2003/12/05 · arxiv updated 2016/08/16
In this work we present 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 resonance 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. The mechanical resonators made the signal ≈ 5340 times stronger. We found i+1 degenerate triplets plus i non-degenerate system mode resonances within a band around 3.17-3.24\rmkHz that are sensitive to signals higher than h∼ 10-22\rmHz-1/2 when we considerate the effects of thermal noise only.