Measurement of added mass for an object oscillating in viscous fluids using nonlinear self-excited oscillations

In this study, a method of measuring the added mass for an object oscillating in a viscous fluid using nonlinear self-excited oscillations was developed. The added mass produces an additional inertial effect on the vibrating object. In previous methods, the added mass is obtained experimentally from the response frequency and amplitude at the peak in the frequency response curve under a harmonically forced excitation. However, such methods cannot be utilized in highly viscous environments because the peak becomes ambiguous as a result of damping. Moreover, in very high-viscosity environments, the resonance peak ceases to exist in the frequency response curves. To solve this problem, self-excited oscillations were induced in the system using linear velocity feedback. Because linear velocity feedback can be used to eliminate the viscous damping effect when the linear feedback gain is set near the Hopf bifurcation point related to self-excited oscillations, the object becomes self-excited at a frequency equal to the natural frequency of the object oscillating in a vacuum, i.e., the undamped natural frequency. What distinguishes the proposed method from the abovementioned previous methods is that the value of the response is not needed; however, a reduction in the oscillation amplitude is required to obtain accurate measurement results. In the proposed method, to avoid an increase in the response amplitude under the applied linear velocity feedback, nonlinear feedback is also applied to produce a limit cycle similar to that produced in a van der Pol oscillator. A prototype of the measurement system was constructed based on the proposed method. A comparison of the experimentally and theoretically obtained added mass values confirmed the validity of the proposed method for added mass sensing.