Eigenfrequencies and quality factors of vibration of aluminium alloy spherical resonators

Abstract

We report the eigenfrequencies and quality factors of vibration of the lowest quadrupole modes of Al 5056 spherical resonators at very low temperatures. Q values of spheroidal modes ranging from 3 × 106 to 2 × 107 in a bulk sample and from 1.7 × 106 to 8 × 106 in an explosively bonded sample were measured. A Q value of 1.2 × 108 was found in a higher order mode of the bulk sample. Independence of the quadrupole modes was measured within one part in 105 in amplitude

Cosmic background of gravitational waves from rotating neutron stars

“…For practical purposes, let us consider a sphere constituted of the aluminium alloy Al-5056. This material has a sound velocity of 5440 ms −1 and Coccia et al (1996) have reported Q values as high as 10 8 for temperatures below 100 mK. A sphere with a diameter of 3.5 m (mass of 60.3 tons) has the two main frequencies of the quadrupole modes at 0.8 kHz and 1.5 kHz, covering quite well the predicted interval where the maximum amplitude of the pulsar background should occur.…”

Techniques for detecting gravitational waves with a spherical antenna

“…6 was surmised on physical grounds, and confirmed by measurements described below. We have not attempted to calculate the magnitude of the splitting caused by the hole, so we cannot make a comparison with the data, however, this effect has subsequently been confirmed by others [23].…”

“…While the effects of deviations from perfect symmetry on a sphere's uncoupled quadrupole modes have been studied [11,22,23], we still need to investigate the effect of asymmetries on our ability to properly interpret the signals from resonant motion sensors. This is why we have kept the equations general until now.…”

“…A second possible cause for a change in mode shape is a hole drilled through the sphere for suspension. However, finite element analysis of a sphere with a hole [21] as well as experiments [22,23] have shown the mode shapes to be changed by less than 1% due to the suspension hole.…”

Deconvolving the information from an imperfect spherical gravitational-wave antenna

“…Imperfections of the sphere can lift the degeneracy causing the modes to "fix" themselves in a particular orientation. This effect has been shown to be the main result of symmetry breaking in an uncoupled sphere; the "shape" of the quadrupole mode remains mostly unchanged [13,14].…”