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An approximate solution of the steady forced vibration of a system of one degree of freedom under the influence of various types of damping¹

Abstract

In this paper the author presents a general method of obtaining approximate solutions of the steady forced vibration of a damped system of one degree of freedom for the case of sinusoidally varying disturbing forces.

The approximation consists in expressing all the damping terms of the original differential equation by a single equivalent damping term, proportional to the first power of the velocity of motion.

In the case of a system influenced by a centrifugal disturbing force and damped by constant friction and by friction proportional to the first power of the velocity, experimental evidence is in good agreement with the approximate solution.

While the paper deals solely with a system of one degree of freedom, there is no reason aside from complexity why the approximate solution cannot be applied to systems of several degrees of freedom.

Footnotes

¹ Contributed by the Applied Mechanics Division for presentation at the semiannual meeting of the American Society of Mechanical Engineers, at Detroit, Michigan, June 9 to 12, 1930. Printed in the Transactions of the American Society of Mechanical Engineers and reprinted here by permission of the editor of the Transactions.