Figure 6

(a) Autonomous 4D SSM model of the nonlinear modal frequency ratio \(\dot{\theta }_2/\dot{\theta }_1\) as a function of amplitudes, along with decaying trajectories (blue, red, yellow). This ratio reaches 4/3 in the regime of the 3-periodic response (purple), signaling that the response originates from this nonlinear 4:3 resonance, as in our analytical example. (b) The periodical samples (red dots) of a forced continuous trajectory (black) lie on a 2D SSM (red). In the reduced coordinates \(\xi _1, \xi _2\) parametrizing the SSM, trajectories converge onto a three-periodic point. (c) SSM prediction of test data for three subsequent periods shows accurate prediction of the sloshing 3-periodic orbit.