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Some Approximations in the Dynamic Shell Equations


El Raheb, Michel Sadek (1970) Some Approximations in the Dynamic Shell Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ejzn-dy90.


A theoretical analysis was performed on the linear dynamic equations of thin cylindrical shells to find the error committed by the Donnell assumption and the neglect of inplane inertia.

The Donnell approximation was found to be valid at high frequencies as compared to the ring frequencies, for all admissible sets of boundary conditions for finite length thin shells.

The error from neglecting tangential inertia is appreciable for long circumferential and axial wave lengths, independent of shell thickness.

The effect of boundary conditions was investigated from an exact solution of the linear eigenvalue problem. The inplane boundary conditions proved to be very influential in the neighborhood of the minimum frequency. An approximate technique which accounts for the inplane boundary conditions was then developed and shown to be in good agreement with the exact solution.

Finally, the effect of an elastic end ring on the eigenfrequencies was studied. The out-of-plane and torsional rigidities of the ring were found to govern the overall shell stiffness. Considerable mode inter action was noticed at low circumferential wave numbers for low values of ring stiffness. The computed eigenfrequencies were found to be in good agreement with the experimental results.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics and Applied Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Babcock, Charles D.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 December 1969
Record Number:CaltechTHESIS:02212013-152121344
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7491
Deposited By: Benjamin Perez
Deposited On:21 Feb 2013 23:36
Last Modified:10 May 2024 21:35

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