Session: 01-08-01: Passive, Semi-Active, and Active Noise and Vibration Control

Paper Number: 145040

145040 - Identification of Maxwell Model Parameters of Viscous Dampers With Elastic Traits 

 

As in polymer-based viscoelastic dampers, fluid viscous dampers exhibit frequency-dependent elastic traits.  This is due to the presence of elasticity in damping fluid molecules, i.e., such fluids exhibit viscoelastic rather than purely viscous behavior. Flow of the fluid deforms the molecules causing a shear-rate dependent elastic response, which over time (determined by the viscous drag on the liquid and the stiffness of the molecules) the molecules relax back to their un-deformed state and the elastic response vanishes.  With such rheology in damping fluid, realistic viscous dampers are not just viscous but viscoelastic devices modeled best by a series combination of pure viscous dampers and springs, known as Maxwell model.

 

Eddy current dampers, which are generally considered as viscous dampers, exhibit frequency-dependent resilience, too.  This is because eddy currents generated in the conductive material by the magnetic field have an inherent time delay (phase lag), i.e., they (eddy currents) do not emerge instantaneously but require time to develop and reach maximum intensity. It arises from the electrical resistance and inductance of the material, causing the eddy currents to lag behind the inducing magnetic field. Consequently, the damping force generated by the eddy current damper experiences a phase lag concerning the motion of the object being damped. Hence, the damping force does not synchronize with the motion but trails it by a certain duration. The extent of this lag depends the characteristics of the conductive material, the magnetic field's strength, and the frequency and magnitude of the damped motion.  These dampers can also be modeled best by a series combination of pure viscous dampers and springs, i.e., Maxwell model.

 

This paper introduces two methodologies for determining Maxwell model parameters for a viscous damper. Both approaches rely on experimental identification employing harmonic displacement loading (sinusoidal loading) across varied excitation frequencies. This entails simultaneous measurement of the damper's displacement and the resultant force to construct its hysteresis curve. By integrating the force with respect to displacement along the hysteresis closed path—representing the area within this path—the energy dissipation of the damper is elucidated.

The first method involves approximating the Maxwell model with a Kelvin-Voigt (K-V) model, evaluating the parameters of the K-V model, and subsequently relating them back to the parameters of the Maxwell model. Conversely, the second method entails determining the phase difference between the measured force and displacement within one cycle. This, coupled with the utilization of the hysteresis curve, enables the direct extraction of Maxwell model parameters. Both methodologies have been employed in identifying the parameters of an eddy current damper at two frequencies, yielding similar results.

Presenting Author: Reza Kashani The University of Dayton

Presenting Author Biography: Reza Kashani received his Ph.D. in Mechanical Engineering from the University of Wisconsin-Madison in 1989.
From 1989 to 1994 he was an assistant professor at Mechanical Engineering-Engineering Mechanics Dept. of Michigan Technological University. He joined The University of Dayton in 1994 where he currently is a full professor at the Mechanical and Aerospace Engineering Department.
Dr. Kashani’s research interests are mainly in control of dynamic systems with special interest in passive and active control of sound and vibration. He has numerous publications in these areas.

Authors:

Abdulrhman Mohmmed H. Farran The University of Dayton
Reza Kashani The University of Dayton