Frequency shift of a rotating mass-imbalance immersed in an acoustic fluid

In this paper, we describe a physical mechanism that relates a measurable behavior of a rigid oscillator device to the physical properties of a surrounding acoustic medium. The device under consideration is a rotating mass imbalance within an enclosed shell that is immersed in an unbounded acoustic fluid. It is assumed that the rotating mass imbalance is driven by an electromagnetic motor excited by a given dc voltage. If nonlinearities are ignored, the steady-state operational frequency of such a device is determined by a balance between the applied electromagnetic and opposing frictional torque on the rotating mass imbalance. If nonlinearities are retained, it is shown that under certain circumstances, the surrounding acoustic medium exerts an additional time-averaged opposing torque on the rotating mass imbalance that reduces the operational frequency of the device. Consequently, the operational frequency of the device becomes linked to the physical properties of the surrounding medium. Analytical calculations showed that the dissipative impedance of an acoustic fluid caused the opposing torque. The shift in frequency is proportional to the dissipative impedance and the square of the rotating mass eccentricity, but inversely proportional the total mass of the device and the damping effect of the dc motor.