Externally excited purely nonlinear oscillators: insights into their response at different excitation frequencies

This study is concerned with forced damped purely nonlinear oscillators and their behaviour at different excitation frequencies. First, their dynamics is considered numerically for the response determined in the vicinity of a backbone curve with the aim of detecting coexisting responses that have not been found analytically so far. Both the cases of low and high excitation amplitudes are investigated. Second, the angular excitation frequency is lowered significantly for different powers of nonlinearity, and the system’s behaviour is examined qualitatively, which has not been considered previously related to a general class of purely nonlinear oscillators. It is illustrated that the response at a low-valued angular excitation frequency has a form of bursting oscillations, consisting of fast oscillations around a slow flow. Finally, approximate analytical solutions are presented for the slow and fast flow for a general class of purely nonlinear oscillators.