SUPPRESSION OF ESCAPE BY RESONANT MODAL INTERACTIONS - IN SHELL VIBRATION AND HEAVE-ROLL CAPSIZE

We establish archetypal equations for studies of internal resonance in systems that can escape from a potential well. In terms of two coordi nates, q(1) and q(2), the potential function, V(q(1),q(2)) = V(-q(1), q(2)), is relevant to a large class of mechanical problems. In particu lar, it arises in the post-buckling of shell structures and in the hea veroll capsize of ships: for the latter we discuss how the V function should be fitted globally to the characteristics of a vessel. With dam ping and external excitation, the coupled nonlinear Lagrange equations are written in a form that allows variation of the internal tuning pa rameter, R, while the form of the potential well remains unchanged. In ternal resonance occurs when R approximate to 2 omega, where omega is the (scaled) driving frequency, and we show that this resonance can si gnificantly suppress the escape. Applied to capsize in beam seas, the results show how nonlinear coupling with heave (or pitch) can influenc e the rolling motions. In particular, we draw the counterintuitive con clusion that capsize can be substantially suppressed when the heave fr equency is tuned to twice the wave frequency.