Masters Theses


"An approximate normal mode method is developed which permits certain normally nondiagonalizable, nonconservative systems to be solved by superposition of uncoupled coordinates.

An approximate solution for a nonproportionally damped, multi-degree of freedom system is obtained by using a perturbation technique. The system is then reduced to a proportionally damped system by means of a modification to the damping factor so that the effect of the off-diagonal terms of the modal damping matrix is included. This modification produces a damping matrix that can be diagonalized by the normal mode technique. An approximate criterion is used for the determination of the modified damping factor….

For the free and transient vibration the approximation criterion selected is that the total energy loss in each mode during the first fundamental period for the nondiagonal system is equal to that for the diagonal system.

To test the accuracy of the mathematical theory, a model is developed. The true response of the model is determined for three different cases: free vibration, transient vibration and forced vibration. Two approximate responses, one by the method discussed in this thesis and the second by ignoring the off-diagonal terms of the modal damping matrix, are also determined for all three cases. The percentage errors between the true response and the approximate responses are evaluated at peak response levels. For the free vibration case examined, the percentage error was smaller when the method presented in this thesis was used than when the off-diagonal terms were neglected. But, for the other two cases examined, no solid conclusions could be drawn for the model tested"--Abstract, pages ii-iii.


Cronin, Don

Committee Member(s)

Koval, Leslie Robert
Cunningham, Floyd M.


Mechanical and Aerospace Engineering

Degree Name

M.S. in Mechanical Engineering


University of Missouri--Rolla

Publication Date



x, 113 pages

Note about bibliography

Includes bibliographical references (page 74).


© 1973 Jayaram Seshadri, All rights reserved.

Document Type

Thesis - Restricted Access

File Type




Subject Headings

Damping (Mechanics)
Perturbation (Mathematics)

Thesis Number

T 2888

Print OCLC #


Electronic OCLC #


Link to Catalog Record

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