Automatic computation of polyharmonic balance equations for non-linear differential systems

An automated algorithm is presented which enables the harmonic balance equations for any polynomial type pure or cross-product non-linear differential system to be written down directly in terms of the coefficients of the governing equation and the complex amplitudes of a general harmonic waveform. The system frequency response, in the form of a multi-input, amplitude dependent describing function, is therefore readily computed. The method is illustrated by means of an example, and the results validated against detailed numeric simulation.