Citation
O'Kelly, Michael Edmond James (1964) Vibration of viscously damped linear dynamic systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd10142002084201
Abstract
A general theory of vibration of damped linear dynamic systems is given. The limitations on the use of the usual normal mode theory in determining the response of damped systems were first studied systematically by Caughey when he derived necessary and sufficient conditions for the uncoupling of systems in Nspace. Systems which cannot be uncoupled in Nspace may still be solvable by modal methods on transforming them to 2Nspace and using the results of Foss. However there exist systems which cannot be solved by the usual modal techniques in either Nspace or 2Nspace. Such systems which include some passive physically realizable systems require the general theory for a complete determination of their motion. For weakly coupled systems the simple perturbation analysis presented gives surprisingly accurate approximations to the actual response of the systems. In any design problem questions of stability arise, particularly when dealing with nonsymmetric systems, and therefore a discussion on the stability of these systems is given.
The second part of the thesis is concerned with linear continuous systems. Exactly solvable continuous systems are rare and in general recourse must be had to numerical methods. The interchangeability of the differential and integral formulation of continuous systems is noted. As in the discrete systems constructive necessary and sufficient conditions are derived for a damped system to possess the same set of complete eigenfunctions as the undamped system. In the discretization of continuous systems the main problem of practical interest is the error bounds on the solution of these discrete approximations when compared to the exact solution. Unfortunately the literature is very poor in this area but what is known is applied to the systems under discussion.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Engineering and Applied Science 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 May 1964 
Record Number:  CaltechETD:etd10142002084201 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd10142002084201 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4074 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  15 Oct 2002 
Last Modified:  26 Dec 2012 03:05 
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