Date of Award

Summer 1965

Degree Type

Thesis - Restricted

Degree Name

Master of Science (MS)



First Advisor

Seireg, Ali

Second Advisor

Matar, Joseph E.

Third Advisor

Pih, Hui


The theory of normal mode vibration is reviewed. The properties of "normal modes" are defined and the transformation of a system to "normal coordinates" is discussed. The transformation enables the response due to an arbitrary excitation of all linear conservative systems and a special class of linear non-conservative systems to be represented as the summation of independent, single degree of freedom "modal" responses. A solution of this form is much simpler than classical methods when excitations are complex or the system has many degrees of freedom. An "Approximate Normal Mode Method" is introduced which permits any linear, non-conservative system to be solved by the method of modal superposition. Accuracy of the Approximate Method was found to be good when checked by digital computer for two-mass systems subjected to steady state sinusoidal and white noise random vibration. Using the Approximate Method a technique is presented which permits a mathematical model for a damped multi-mass system to be constructed entirely from experimentally obtained, sinusoidal frequency response data. Optimum system parameters are considered for a two-mass system. The results of Den Hartog and Brock for steady state sinuisoidal excitation are reviewed. Expressions are derived for optimum damping mass ratio and natural frequency ratio that will minimize the response of the same system to white noise random excitation.