Mode-dependent mechanical losses in disc resonators

Mechanical spectroscopy gives information on the structure of solids and their relaxation mechanisms through the measurements of the elastic constants and the mechanical loss angle of materials. One common way to estimate these quantities is the resonant method where the frequency and the characteristic decay time of oscillations are measured. Since many solid materials can be easily found in the shape of thin disc we have investigated the mechanical loss of these resonators and we have found experimentally that the loss angle dependence on the mode is not trivial but rather follow a distribution of modes into families. We give a model that is able to justify the existence of these families and to predict the level of losses in silicon, silica and brass discs. The model considers the thermoelastic effect and the excess damping caused by the condition of the disc edge. The results of this research are relevant to the research on thin films that are deposited on thin discs like the optical coatings used on the mirrors for the gravitational wave detectors.