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Nonlinear Vibration of Cylindrical Shells


Chen, Jay-Chung (1972) Nonlinear Vibration of Cylindrical Shells. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CBC4-MP23.


The large amplitude vibrations of a thin-walled cylindrical shell are analyzed using the Donnell's shallow-shell equations. A perturbation method is applied to reduce the nonlinear partial differential equations into a system of linear partial differential equations. The simply-supported boundary condition and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental modes, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental modes. In the previous investigations in which the Galerkins procedure was applied, only the additional axisymrnetric modes were assumed. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. The region where the companion mode participates in the vibration is obtained and the effects due to the participation of the companion mode are studied. An experimental investigation is also conducted. The results are generally in agreement with the theory. "Non-stationary4 response is detected at some frequencies for large amplitude response where the amplitude drifts from one value to another. Various nonlinear phenomena are observed and quantitative comparisons with the theoretical results are made.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Babcock, Charles D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:14 December 1971
Record Number:CaltechTHESIS:09242010-085617930
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6049
Deposited By: Dan Anguka
Deposited On:24 Sep 2010 16:33
Last Modified:28 Jun 2024 22:05

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