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Measurement of added mass for an object oscillating in viscous fluids using nonlinear self-excited oscillations
Nonlinear Dynamics ( IF 5.6 ) Pub Date : 2020-11-25 , DOI: 10.1007/s11071-020-06087-3
Jiahao Yang , Hiroshi Yabuno , Naoki Yanagisawa , Yasuyuki Yamamoto , Sohei Matsumoto

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.



中文翻译:

使用非线性自激振荡测量在粘性流体中振荡的物体的附加质量

在这项研究中,开发了一种使用非线性自激振荡来测量在粘性流体中振荡的物体的附加质量的方法。增加的质量在振动的物体上产生附加的惯性作用。在以前的方法中,在谐波强制激励下,根据频率响应曲线中峰值处的响应频率和幅度,通过实验获得附加质量。但是,由于阻尼导致峰值变得不明确,因此无法在高粘度环境中使用此类方法。此外,在非常高粘度的环境中,共振峰不再存在于频率响应曲线中。为了解决这个问题,使用线速度反馈在系统中引起了自激振荡。由于在将线性反馈增益设置为与自激振荡相关的霍普夫分叉点附近时,可以使用线速度反馈消除粘性阻尼效应,因此对象会以与对象振荡的固有频率相等的频率自激在真空中,即无阻尼的固有频率。所提出的方法与上述先前方法的区别在于不需要响应的值。但是,需要减小振荡幅度以获得准确的测量结果。在提出的方法中,为避免在施加的线速度反馈下响应幅度增加,还应用了非线性反馈以产生类似于范德波尔振荡器中产生的极限周期。基于所提出的方法构造了测量系统的原型。实验和理论上获得的附加质量值的比较证实了所提出的附加质量感测方法的有效性。

更新日期:2020-11-25
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