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Free and Forced Oscillations in a Class of Piecewise-Linear Dynamic Systems


Vijayaraghavan, Alwar (1971) Free and Forced Oscillations in a Class of Piecewise-Linear Dynamic Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/11SF-5Q09.


A study is made of the free and forced oscillations in dynamic systems with hysteresis, on the basis of a piecewise-linear, nonlinear model proposed by Reid. The existence, uniqueness, boundedness and periodicity of the solutions for a single degree of freedom system are established under appropriate conditions using topological methods and Brouwer's fixed-point theorem. Exact periodic solutions of a specified symmetry class are obtained and their stability is also examined. Approximate solutions have been derived by the Krylov-Bogoliubov-Van der Pol method and comparison is made with the exact solutions.

For dynamic systems with several degrees of freedom, consisting of "Reid oscillators", exact periodic solutions are derived under certain restricted forms of "modal excitation" and the stability of the periodic solutions has been studied. For a slightly more general form of sinusodial excitation, a simple way of obtaining approximate solutions by "apparent superposition" has been indicated. Examples are presented on the exact and approximate periodic solutions in a dynamic system with two degrees of freedom.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mechanical Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Caughey, Thomas Kirk
Thesis Committee:
  • Unknown, Unknown
Defense Date:4 December 1970
Funding AgencyGrant Number
Woodrow Wilson FoundationUNSPECIFIED
Ford FoundationUNSPECIFIED
Record Number:CaltechTHESIS:12062017-105553336
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10590
Deposited By: Benjamin Perez
Deposited On:06 Dec 2017 19:33
Last Modified:21 Dec 2019 01:53

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