Effects of Extra Sinusoidal Inputs to Nonlinear Systems

[+] Author and Article Information
R. Oldenburger

Mechanical Engineering, Purdue University, Lafayette, Ind.

R. C. Boyer

Purdue University, Lafayette, Ind.

J. Basic Eng 84(4), 559-569 (Dec 01, 1962) (11 pages) doi:10.1115/1.3658710 History: Received July 14, 1961; Online November 04, 2011


This paper presents a technique for predicting the effect of an extra high frequency sinusoidal input on systems with various commonly occurring types of nonlinearities. This input may be thought of as an extra input introduced into a system to improve the performance of nonlinear components. The mathematical analysis is greatly simplified by the introduction of a certain approximation to the input-output relationship of a nonlinear element when the input to the nonlinear element is the sum of the regular sinusoidal input signal and an extra sinusoidal signal of higher frequency. For the approximation to be valid experience and theory indicate that the ratio between the frequencies of the sinusoidal inputs should be on the order of ten or more. The extra sinusoidal input may reduce or remove the hunt (self-oscillation) of some systems, but it may create a hunt in others. In computations, a nonlinear element with an extra sinusoidal input may often be replaced by an equivalent nonlinear element without the extra input. By introducing the extra input a designer may be saved the expense of physically replacing one nonlinear component by another, the input-output characteristics of the first being transformed by the extra input into the characteristics of the second. The introduction of an extra signal may yield much better transient response than is possible by changing open loop gain. Examples are given with analog computer verification.

Copyright © 1962 by ASME
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