Nonlinear Dynamics and Internal Resonances of a Ship With a Rectangular Cross-Section in Head Seas

Abstract

Finite amplitude dynamics of ships in head seas due to parametric instabilities is a subject of renewed interest with an increasing demand of operation in severe and variable environmental conditions. In this current study we investigate the nonlinear dynamics and internal resonances of a ship with a rectangular cross-section in head seas. We employ an asymptotic averaging method to obtain the slowly varying system evolution dynamics for the weakly nonlinear response, complemented by numerical integration in the strongly nonlinear regime. A weakly nonlinear frequency response is obtained analytically for a principal parametric resonance and a 1:1 roll—pitch internal resonance. Comparison of results with three degrees of freedom numerical simulations reveals a good fit. A strongly nonlinear numerical analysis reveals that beyond the stability thresholds, the system’s responses included quasiperiodic dynamics. This combined approach resolves both parametric instabilities and internal resonances induced for both weak and finite nonlinear interactions, and culminates with criteria for orbital stability thresholds describing the onset of quasiperiodic response and magnification of energy transfer between coupled pitch-heave and ship roll.

Non-linear model-based estimation of quadratic and cubic damping mechanisms governing the dynamics of a chaotic spherical pendulum

“…The documentation of non-linear damping in dynamical systems undergoing flow-structure interaction is not new. Examples include viscous effects that yield for high Reynolds numbers a resistance proportional to the square of the velocity (Tritton, 1977) that governs aeroelastic drag (Dowell and Tang, 2003) and ship roll damping (Kleiman and Gottlieb, 2009). In addition to the common two-term linear and quadratic formulations first proposed by Froude (1955), equivalent linear and cubic damping models have also been analyzed asymptotically (Cardo et al, 1982) and globally (Bikdash et al, 1994).…”