A Comparison between the Fourier and Ritz Describing Functions for the Damped Driven Duffing Equation

Fourier and Ritz describing functions are obtained for the damped, driven Duffing equation. These results are compared to the pseudo-describing function, which is defined as the ratio of the first harmonic output amplitude obtained with a real filter to the input amplitude. The results indicate that the Ritz describing function is a better approximation to the pseudo-describing function. Since a number of important nonlinear systems can be represented or approximated by the Duffing equation, it seems that the Ritz describing function has significance as another tool in nonlinear system analysis.