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Analog Methods of Nonlinear Vibration Analysis


Greenwood, Donald Theodore (1951) Analog Methods of Nonlinear Vibration Analysis. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0DNR-VB14.


This thesis presents methods by which electrical analogies can be obtained for nonlinear systems. The accuracy of these methods is investigated and several specific types of nonlinear equations are studied in detail.

In Part I a general method is given for obtaining electrical analogs of nonlinear systems with one degree of freedom. Loop and node methods are compared and the stability of the loop analogy is briefly considered.

Parts II and III give a description of the equipment and a discussion of its accuracy. Comparisons are made between experimental and analytic solutions of linear systems.

Part IV is concerned with systems having a nonlinear restoring force. In particular, solutions of Duffing's equation are obtained, both by using the electrical analogy and also by approximate analytical methods.

Systems with nonlinear damping are considered in Part V. Two specific examples are chosen: (1) forced oscillations and (2) self-excited oscillations (van der Pol’s equation). Comparisons are made with approximate analytic solutions.

Part VI gives experimental data for a system obeying Mathieu's equation. Regions of stability are obtained. Examples of subharmonic, ultraharmonic, and ultrasubharmonic oscillat1ons are shown.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Physics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McCann, Gilbert Donald
Thesis Committee:
  • Unknown, Unknown
Defense Date:1951
Record Number:CaltechTHESIS:03242016-111828484
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9633
Deposited By: Bianca Rios
Deposited On:25 Mar 2016 14:30
Last Modified:02 May 2023 16:45

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