Chapter 2 - Harmonic balance method and time domain collocation method

Abstract

In this chapter we take the Duffing equation as example to illustrate that the subharmonic oscillations (when the period of the forcing function is nearly three times the natural frequency of the linear system) can be captured by using the time collocation method over a period, assuming harmonic as well as subharmonic Fourier series as the trial functions. We show that the present simple notion of collocation of the error in the nonlinear ODE, with the assumed trial functions, is entirely equivalent to the high-dimensional harmonic balance (HDHB) method or the time domain harmonic balance (HB) method.