Session: MSNDC-04-01 Nonlinear Dynamics of Structures

Paper Number: 74420

Start Time: August 17, 11:10 AM

74420 - Nonlinear Viscometer Based on a Cantilever Self-Excited in Rayliegh-Type Oscillation 

Resonating cantilever beams have been widely used as resonators in vibration-type viscometers. The attenuation ratio of a free oscillation of the resonator in a measured sample is an important parameter to show the viscosity. The past measurement techniques using the peak frequency of a frequency response curve under external excitation are for detecting the linear component of the viscosity. However, the cubic nonlinear component is also important in samples with high viscosity.

In this work, we propose a self-excitation method using feedback control with respect to the velocity of the resonator to detect the cubic nonlinear component of the viscosity in a measured sample. In our previous studies, the dependence of the critical linear feedback gain to produce the self-excited oscillation on the linear component of the viscosity is theoretically and experimentally shown. We consider the nonlinear feedback to detect the cubic nonlinear component and derive the method to detect the nonlinear component by using the bifurcation diagram, that is the relationship between the response amplitude and the linear feedback gain, whose slope is changed by tuning the nonlinear feedback gain. We propose a self-excited oscillating viscometer based on a cantilever beam; the free end has a sensing slice, which can move in the direction perpendicular to the direction of the cantilever displacement. The displacement signal of the cantilever is fed back to a piezoelectric actuator providing a displacement excitation to the supporting point of a cantilever. To detect the cubic nonlinear component of the viscosity, we apply the nonlinear feedback method to produce the Rayliegh-type self-excited oscillation. Finally, we carry out experiments using the cantilever sensor to detect the viscosity in air and viscous fluid and identify the cubic nonlinear component of the viscosity in the viscous fluid. The proposed method is very promising for viscosity measurement in high-viscous environment because the cubic nonlinear component of the viscocsity can be detected by applying the method of nonlinear feedback control.

Presenting Author: Keyu Zhou University of Tsukuba

Authors:

Keyu Zhou University of Tsukuba
Hiroshi Yabuno University of Tsukuba