A Study of the Effects of Damping on Normal Modes of Electrical and Mechanical Systems

Citation

Crumb, Stephen Franklin (1955) A Study of the Effects of Damping on Normal Modes of Electrical and Mechanical Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YESX-K771. https://resolver.caltech.edu/CaltechETD:etd-12042003-110450

Abstract

This thesis is a general investigation of some of the properties of free and forced vibrations in linear, non-conservative systems. Particular emphasis is placed upon the problems which arise in normal mode studies made on the electric analog computer at the California Institute of Technology. In Part I the major problems are defined, and limitations of the study are discussed. Part II is a review of the basic theory of normal modes included primarily to establish familiarity with the notation to be used later. In Part III, modifications of normal mode concepts, as applied to damped systems, are examined. "Small damping" criteria are discussed, and a set of theorems of small damping is presented. In Part IV a series of normal mode analog circuits for damped systems are developed. Part V is a study of uniform damping, generalizing and extending some of the work of Rayleigh, Bode, and Guillemin. It is shown that for any type of uniform damping, all of the basic normal mode concepts are preserved. In Part VI the theory of mode separation in uniformly damped systems is considered. Criteria for determining mode frequencies and mode parameters are developed. A multiple drive method of exciting normal modes is proposed. In Part VII, some of the methods of Part VI are extended to non-uniformly damped systems. Equivalent orthogonal systems are proposed to approximate the behavior of systems with moderately non-uniform damping. A quantitative measure of non-uniformity is presented. In Part VIII, numerical examples and experimental results in support of the theory are presented. Concluding remarks are made in Part IX.

Thesis Files