On the effects of asymmetry on the primary resonance response of a pure cubic duffing oscillator

Abstract

The primary resonance response of a system with no linear restoring term and with cubic hardening non-linearity is investigated in this paper. The system is subject to both a harmonic and a constant excitation. The appearance of different shapes of frequency-response curves and multiple jumps is considered. A parametric analysis is presented to indicate the influence of asymmetry caused by the constant force on the onset of these phenomena. For this purpose, the method of harmonic balance is used. Numerical simulations are also carried out to confirm the analytical results.