Rotational galloping of two coupled oscillators
The authors consider nonlinear rotational galloping for two mechanically coupled see-saw oscillators in steady cross-flow, and they obtain two nonlinearly coupled harmonic oscillators using a quasi-steady modelling approach. The authors find either a non-resonant (for strong coupling) or 1:1 internal resonant system (for weak coupling) depending on \(K\), the order of the mechanical coupling, and on the difference \(\delta\) between the natural frequencies of the uncoupled oscillators. The averaged equations in the case of weak coupling allow stable limit cycles which arise in symmetrical pairs and are born by Hopf bifurcations. In addition, numerical calculations suggest that for certain parameter values these cycles may merge into large symmetrical limit cycles, and that all the limit cycles found for the averaged equations correspond to solutions with periodically modulated amplitudes and phases for the original system.
scientific article; zbMATH DE number 1240529