Support loss for beam undergoing coupled vibration of bending and torsion in rocking mass resonator

Rocking mass resonator is widely used to design various sensors and actuators, which is a dual-axial symmetry resonator with high sensitivity. Q_support is the dominant energy loss mechanism influencing its high sensitivity. The anchor types and support loads applied to attachment points of rocking mass resonator are analyzed. Then support loss is simplified as a model with a beam attached to a finite thickness plate at its end. The general formulations for power radiated into support structure are given. An accurate analytical model of support loss for rocking mass resonator has been developed and verified by experiments. When the thickness of resonator is 240 μm, the measured Q can achieve a value of 589.1; while the thickness of resonator is reduced to 60 μm, the measured Q can achieve a value more than 8500. The derived model is general and might be applicable to various micro beam resonators and anchor types, providing significant insight to design of high-Q rocking mass devices.