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Dynamic response of hysteretic systems with application to a system containing limited slip

Furuike, Dennis Masato (1971) Dynamic response of hysteretic systems with application to a system containing limited slip. California Institute of Technology . (Unpublished)

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A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined. An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop. The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip. To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first, Then the relationship between initial conditions and, resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

Item Type:Report or Paper (Technical Report)
Additional Information:PhD, 1972
Group:Dynamics Laboratory
Record Number:CaltechEERL:1971.DYNL-105
Persistent URL:
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:26453
Deposited By: Imported from CaltechEERL
Deposited On:14 May 2002
Last Modified:03 Oct 2019 03:14

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