Duffing-type nonlinear oscillators: insight into dynamic phenomena via backbone curves and frequency-amplitude plots Seminar

Abstract:

Duffing-type nonlinear oscillators are characterised by the existence of cubic geometric nonlinearity in their equation of motion. The frequency of their free oscillations changes with the amplitude. Consequently, their backbone curve, which is a graphical presentation of the relationship between the natural frequency and the amplitude, is bent. When these oscillators are externally excited, the primary frequency-amplitude plot around the backbone curve is also bent, and associated with certain nonlinear phenomena, such as multiple coexisting steady-state responses and sudden discontinuous changes (jumps) of the amplitude. Some possible shapes and characteristics of backbone curves and the corresponding frequency-amplitude plots are presented for the Duffing-type systems with one and two degrees of freedom. It is also shown how one can use nonlinearity to unbend a backbone curve of Duffing-type oscillators to make it be straight as in the linear oscillator.

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