Acoustic resonance widening in GW detectors: detailed modelling of the dissipation processes

Internal friction effects are responsible for line widening of the acoustic resonance frequencies in mechanical oscillators and result in damped oscillations of its eigenmodes with a decay time Q/(omega). We study the solutions to the equations of motion for the case of spherical oscillators, to be used as the next generation of acoustic gravitational wave detectors, based on various different assumptions about the materialʹs constituent equations. Quality factor dependence on mode frequency is determined in each case, and a discussion of its applicability to actual gravitational wave detectors is made on the basis of available experimental evidence.