  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 $\approx 5340$ times
stronger. We found $i+1$ degenerate triplets plus $i$ non-degenerate system
mode resonances within a band around ${3.17-3.24\rm{kHz}}$ that are sensitive
to signals higher than ${\tilde h\sim 10^{-22}\rm{Hz}^{-1/2}}$ when we
considerate the effects of thermal noise only.
