Nonlinear Dynamical Model for Hysteresis Based on Nonconvex Potential Energy
Publication: Journal of Engineering Mechanics
Volume 133, Issue 5
Abstract
A model for hysteretic dynamics is proposed in the current paper. Hysteresis is treated as an input–output relation for a dynamic system. The Lagrangian of the dynamic system is constructed on the basis of a nonconvex potential energy and governing equations of the system dynamics are obtained using the Lagrangian equation. Bifurcations will be induced in the nonlinear dynamics due to the nonconvexity of the potential energy. It is shown that when the coefficients are chosen appropriately, the bifurcation diagram will lead to hysteretic behavior. Both the third- and fifth-order nonlinear terms are investigated and it is shown that the fifth-order nonlinearity is able to give a perfect prediction of experimental hysteretic behaviors. Hysteretic damping force of a magneto-rheological fluid damper and polarization hysteresis in piezoelectric materials are modeled successfully using the current model. The parameter identification for the model is also presented.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 5 • May 2007
Pages: 506 - 513
Copyright
© 2007 ASCE.
History
Received: Jan 26, 2006
Accepted: Aug 2, 2006
Published online: May 1, 2007
Published in print: May 2007
Notes
Note. Associate Editor: George Z. Voyiadjis
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