Analysis of quadrupolar frequencies of the spherical gravitational wave detector by finite element modeling: A study case

The Schenberg detector is a spherical resonant antenna gravitational wave detector with a solid sphere with a diameter of 65 cm and a weight of approximately 1.15 metric tons. It is made of a copper–aluminum alloy with 94% Cu and 6% Al. This work aims to verify the natural frequencies of the Schenberg detector structure. The authors used the finite element method to calculate the quadrupole frequency band and compare it with the value measured in tests during the construction of the antenna at University of Sao Paulo, which was 67.3 Hz. In the modal simulation with the homogenous material, the frequency band of the quadrupole modes was around 35 Hz. Many trials to improve this result were made with no significant improvement. The improvement came when the sphere was considered not homogenous, as to the cooling process of the sphere casting, the alloy that cooled faster (close to the surface sides and in the bottom) can reach a hardness 20% higher than the material that cooled slower (in the center and on the top). Including these characteristics, the band value obtained was close to the one measured during the construction of the antenna, a value of 63.2 Hz was obtained.