Higher harmonic oscillations in heteronomous non-linear systems with one degree of freedom

Abstract Higher harmonic oscillations in systems governed by Duffing-type differential equations are investigated by the harmonic balance method and by an analog computer analysis. Theoretical resonance curves of the first and third harmonic components of the response, the amplitudes and phase angles of which vary with the frequency of external force, are analyzed and compared with analog computer results. The stability problem is analyzed by solving a corresponding variational Hill-type equation. Regions of anomalous generation of the third harmonic component and of even and odd higher harmonic components, termed higher order resonances, as found through analog computer techniques are found, and phenomena analogous to that at the main resonance (“jump” and hysteresis effects) are observed.