A Describing Function for Dynamic Forces in Single Degree-of-Freedom Mechanisms

Abstract

In a single degree-of-freedom mechanism, a generalized force is produced by elastic, dissipative, and inertial effects. This force may be expressed as a power series in the mechanism’s generalized velocity where the coefficients are functions of the generalized displacement. Approximating the coefficients by their Fourier series expansions produces a describing function which is rapidly convergent and provides substantial computational and analytical advantages over using the exact equations. This describing function permits efficient time-domain simulation of mechanism dynamics and produces an analytical expression for the spectral content of the mechanism dynamic force. Generation and application of the describing function is illustrated by a numerical example.