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Free and Forced Oscillations of a Class of Self-Excited Oscillators


Malhotra, Rajeshwar Kumar (1965) Free and Forced Oscillations of a Class of Self-Excited Oscillators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/81MF-FT73.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Free and forced oscillations in oscillators governed by the equation [...] are studied with appropriate constraints on [...]. Theorems are proved on the existence and uniqueness of stable periodic solutions for free oscillations using the Poincare-Bendixson theory in the phase-plane. There follow several examples to illustrate the theorems and limit cycles are obtained for these examples by the Leinard construction. A result on the existence of periodic solutions in the forced case is obtained by use of Brouwer's fixed point theorem. The part on topological methods is concluded by applying Yoshizawa's results on ultimate boundedness of solutions to the forced case. Approximate analytical solutions are obtained for specific examples for different regions of validity of the parameter [...]. For free oscillations, the perturbation solution is obtained for small [...]. A Fourier series approximation is given for other values of [...] and the limit cycle for the case [...] is obtained. Finally, the first order solution for forced oscillations is obtained by the method of slowly varying parameters and the stability of this solution is examined.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Caughey, Thomas Kirk
Thesis Committee:
  • Caughey, Thomas Kirk (chair)
  • Hudson, Donald E.
  • Housner, George W.
  • Knowles, James K.
  • Sabersky, Rolf H.
Defense Date:25 September 1964
Record Number:CaltechETD:etd-10012002-092546
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3842
Deposited By: Imported from ETD-db
Deposited On:02 Oct 2002
Last Modified:09 Feb 2024 00:37

Thesis Files

PDF (Malhotra_r_1965.pdf) - Final Version
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