Lumped Parameter Analogies for Continuous Mechanical Systems

Author: Russell, William Treloar

Year: 1950

Degree: Dissertation (Ph.D.)

Advisor: Housner, George W.

Committee Member: Unknown, Unknown

Option: Mechanical Engineering; Electrical Engineering

DOI: 10.7907/pv3j-w995

Abstract

This thesis is an investigation of the analogies between lumped or continuous mechanical systems and electric circuits. Methods are developed for obtaining electric circuit analogs of linearized mechanical systems. Essential features of the development are the use of coordinate transformations and the transformation properties of certain fundamental matrices. These make possible a general treatment of the problem of obtaining efficient analogs.

The general theory is developed in part II and it is shown that an electric circuit using linear passive, bi-lateral elements and ideal transformers may be constructed for any of the linear mechanical systems considered.

In part III a new approach to the problem of circuit analogies for beams is developed and the methods of part II are applied to obtain new and more accurate analogies for the dynamic behavior of beams with up to six degrees of freedom. A discussion of analogies for frames is given and the effects of the so-called shear deflection and of combined lateral and axial loads in beams is investigated.

In part IV the errors due to lumping of distributed mass and distributed external force are investigated for some simple systems.

A discussion and summary of the thesis is given on pages 11 to 14.

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