On the modes and loss mechanisms of a high Q mechanical oscillator

We have performed laser-Doppler vibrometry measurements of the vibration of a double-paddle oscillator. Seven modes with principally out-of-plane motion have been identified. Their resonance frequencies and mode shapes are in excellent agreement with three-dimensional finite element simulations. We have found that the second antisymmetric torsional mode has exceptionally good vibration isolation of its mode shape. This explains its extremely small low temperature internal friction below 10 K ${\text{(2×10}}^{\text{−8}}\mathrm{).}$ By correlating the internal friction of each mode with features of their mode shapes, a criterion has been established to develop high Q oscillators.