In this work we present a mathematical model for the mechanical response ofthe Brazilian Mario SCHENBERG gravitational wave (GW) detector to such waves.We found the physical parameters that are involved in this response assuming alinear elastic theory. Adopting this approach we determined the system'sresonance frequencies for the case when six $i$-mode mechanical resonators arecoupled to the antenna surface according to the arrangement suggested byJohnson and Merkowitz: the truncated icosahedron configuration. Thisconfiguration presents special symmetries that allow for the derivation of ananalytic expression for the mode channels, which can be experimentallymonitored and which are directly related to the tensorial components of the GW.Using this model we simulated how the system behaves under a gravitationalsinewave quadrupolar force and found the relative amplitudes that result fromthis excitation. The mechanical resonators made the signal $\approx 5340$ timesstronger. We found $i+1$ degenerate triplets plus $i$ non-degenerate systemmode resonances within a band around ${3.17-3.24\rm{kHz}}$ that are sensitiveto signals higher than ${\tilde h\sim 10^{-22}\rm{Hz}^{-1/2}}$ when weconsiderate the effects of thermal noise only.
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机译：在这项工作中，我们提出了巴西Mario SCHENBERG重力波（GW）检测器对此类波的机械响应的数学模型。我们假设非线性弹性理论，发现了该响应所涉及的物理参数。采用这种方法，我们根据Johnson和Merkowitz建议的布置（截短的二十面体配置），确定了当六个$ i $模式机械谐振器耦合到天线表面时的系统谐振频率。这种配置呈现出特殊的对称性，可以导出模式通道的解析表达式，可以通过实验监控其并与GW的张量分量直接相关。使用此模型，我们模拟了系统在重力正弦波四极力下的行为激发产生的相对振幅。机械谐振器使信号约5340倍。我们发现$ i + 1 $个退化的三元组加上$ i $个非退化的系统模式共振在$ {3.17-3.24 \ rm {kHz}} $附近的一个波段内，对高于$ {\ tilde h \ sim 10 ^ {仅考虑热噪声的影响时，为-22} \ rm {Hz} ^ {-1/2}} $。
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