Obtaining the frequencies of Schenberg detector sphere using finite element modelling

Abstract

The resonant-mass gravitational wave detector SCHENBERG is a spherical detector that operates with a central frequency close to 3200 Hz and a bandwidth around 200 Hz. It has a spherical mass that works as an antenna whose weight is 1150 kg and is connected to the outer environment by a suspension system designed to attenuate local noise due to seism as well as other sources; the sphere is suspended by its center of mass. When a gravitational wave passes by the detector, the antenna is expected to vibrate. This motion should be monitored by six parametric microwave transducers whose output signals will be digitally analyzed. In order to determine the detector performance better, it is necessary to obtain the vibration frequencies of the sphere with a better precision. To achieve such a goal the sphere with the holes to mount the transducers and the central hole from which the sphere is suspended is simulated in a finite element method program when the gravity is applied to the sphere and the deformation is kept. After that the vibration normal modes of the sphere are calculated and they are compared to the experimental results.