Coexisting attractors in floating body dynamics undergoing parametric resonance

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

A New Method to Predict Vessel Capsizing in a Realistic Seaway

A recently developed approach, in the area of nonlinear oscillations, is used to analyze the single degree of freedom equation of motion of a oating unit (such as a ship) about a critical axis (such as roll). This method makes use of a closed form analytic solution, exact upto the rst order, and takes into account the the complete unperturbed (no damping or forcing) dynamics. Using this method very-large-amplitude nonlinear vessel motion in a random seaway can be analysed with techniques similar to those used to analyse nonlinear vessel motions in a regular (periodic) or random seaway. The practical result being that dynamic capsizing studies can be undertaken considering the shortterm irregularity of the design seaway. The capsize risk associated with operation in a given sea state can be evaluated during the design stage or when an operating area change is being considered. Moreover, this technique can also be used to guide physical model tests or computer simulation studies to focus on critical vessel and environmental conditions which may result in dangerously large motion amplitudes. Extensive comparitive results are included to demonstrate the practical usefulness of this approach. The results are in the form of solution orbits which lie in the stable or unstable manifolds and are then projected onto the phase plane

Analytical and experimental investigations of ships impact interaction with one-sided barrier

This study deals with impact interaction of ships with one-sided ice barrier during roll dynamics. An analytical model of ship roll motion interacting with ice is developed based on Zhuravlev and Ivanov non-smooth coordinate transformations. These transformations have the advantage of converting the vibro-impact oscillator into an oscillator without barriers such that the corresponding equation of motion does not contain any impact term. Such approaches, however, account for the energy loss at impact times in different ways. The present work, in particular, brings to the attention the fact that the impact dynamics may have qualitatively different response characteristics to different dissipation models. The difference between localized and distributed equivalent damping approaches is discussed. Extensive numerical simulations are carried out for all initial conditions covered by the ship grazing orbit for different values of excitation amplitude and frequency of external wave roll moment. The basins of attraction of safe operation are obtained and reveal the coexistence of different response regimes such as nonimpact periodic oscillations, modulation impact motion, period added impact oscillations, chaotic impact motion and rollover dynamics. An experimental investigation conducted on a small ship model. In particular, the experimental tests reveal complex dynamic response on multi-frequency wave motion caused by the wave reflection from the tank walls. Measured results showed a good agreement with the predicted results for small angles of the barrier relative to the ship unbiased position. However, deviation becomes significant as the angle increases. This deviation is mainly attributed to the uncertainty of the coefficient of restitution, which is found to depend on the velocity of impact in addition to the geometry and material properties of the model and barrier

Stability analysis of floating raft system under multiexcitation condition

A floating raft system is subjected to multiple excitation sources with multiple frequencies for each excitation source. Considering the two characteristics of excitation source, the stability of floating raft system was analyzed. A vibration equation for the floating raft system under multiexcitation condition was established. A multiscale method was then used to solve the equation. The amplitude–frequency response equation and unstable region of solution are discussed. The results show that the vibration of raft frame fits the pattern of soft-spring vibration. This indicates that the excitation of main raft unit with a rigid connection compromises the stability of the system, whereas the excitation of unit with elastic connection increases stability

Models, Methods, and Applications of Dynamics and Control in Engineering Sciences: State of the Art

Guest editor, numero speciale di Mathematical Problems in Engineerin