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Dynamic Response of Hysteretic Systems with Application to a System Containing Limited Slip


Furuike, Dennis Masato (1972) Dynamic Response of Hysteretic Systems with Application to a System Containing Limited Slip. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/WENT-KG11.


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:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Iwan, Wilfred D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:17 September 1971
Funding AgencyGrant Number
Fannie and John Hertz FoundationUNSPECIFIED
Record Number:CaltechTHESIS:04082016-132302337
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9662
Deposited On:08 Apr 2016 21:15
Last Modified:01 Jul 2024 17:13

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