Coexisting attractors in floating body dynamics undergoing parametric resonance

Abstract

This study pertains to analysing the dynamical behaviour of a floating body undergoing parametric resonances. A simple vertical cylinder, representing a classical spar-buoy, is considered, limiting its motion to heave and pitch degrees of freedom. Its geometry and mass distribution are chosen such that a 2:1 ratio of heave to pitch/roll natural frequency makes the spar-buoy prone to parametric resonance. The system is then studied by the shooting method, combined with a pseudo-arclength continuation, and the harmonic balance procedure. Results show that an extensive bistable region exists, where stable parametric resonance coexists with a regular resonance response. The analysis also unveiled the existence of stable quasiperiodic motions existing in correspondence of both pitch and heave resonance. Results are qualitatively validated using a model based on the explicit nonlinear Froude–Krylov force calculation.

Parametric excitation suppression in a floating cylinder via dynamic vibration absorbers: a comparative analysis

“…where F I,i is the inertia, F R,i is the hydrostatic restoring force, F D,i is the hydrodynamic damping force and F E,i is the wave excitation force. In addition to the experimental validation performed in [38], the ability of this hydrodynamic model to correctly predict parametric resonance is also verified in a code-to-code comparison against a NLFK model in [57].…”

“…We remark some limitations of the implemented HBM for the system under study. First of all, neglecting higher harmonics and constant terms (harmonics of order zero) might have an effect on the system dynamics, especially at high amplitude [57]. However, for the analysed cases, the considered harmonic components seemed sufficient.…”

“…Furthermore, the procedure studies only periodic solutions, while nonlinear systems, and especially NESs, typically exhibit quasiperiodic motions, relaxation oscillations [72] or even chaotic motions [73], completely overlooked by the HBM adopted. Additionally, the procedure is unable to identify coexisting branches of periodic solutions [57]; it would be possible to implement control schemes to partially analyse if more branches coexist; however, considering the already high computational cost of the analysis, we decided not to implement such techniques. Finally, the HBM is not effective for studying multifrequency sea spectra and cannot be used for the irregular wave simulations.…”

A Computationally Efficient Analytical Modelling Approach for Parametric Oscillations in Floating Bodies

“…A review of these types of nonlinear hydrodynamic models, whose computational expense and modelling accuracy sit between the linear potential flow and the RANS equations methods is given in [34]. The most commonly used of these methods for simulating parametric resonance in floating bodies is the Nonlinear Froude-Krylov (NLFK) model [35][36][37][38][39][40][41][42][43][44][45][46] which extends the conventional linear hydrodynamic model by calculating the Froude-Krylov force (the integral of the pressure from the undisturbed wave-field) at each time step based on the evolving instantaneous (rather than the mean) wetted-surface of the body. Compared to a RANS-based CFD simulation for predicting the occurrence of parametric resonance in a floating cylinder, a NLFK model is reported to be more than 5000 times faster with similar accuracy [46].…”

Combining pendulum and gyroscopic effects to step-up wave energy extraction in all degrees of freedom

“…Nevertheless, such models should preserve the inherent passive characteristics of the system [15], while remaining able to articulate typical instabilities of floating structures, e.g. parametric resonance [16] or yaw instability [17]. Finally, due to the resulting potential complexity of such nonlinear models, it is often convenient to apply model order reduction techniques to achieve real-time computation, required for practical implementation [18].…”