A Body-Nonlinear Green's Function Method with Viscous Dissipation Effects for Large-Amplitude Roll of Floating Bodies

A novel time-domain body-nonlinear Green’s function method is developed for evaluating large-amplitude roll damping of two-dimensional floating bodies with consideration of viscous dissipation effects. In the method, the instantaneous wetted surface of floating bodies is accurately considered, and the viscous dissipation effects are taken into account based on the “fairly perfect fluid” model. As compared to the method based on the existing inviscid body-nonlinear Green’s function, the newly proposed method can give a more accurate damping coefficient of floating bodies rolling on the free surface with large amplitudes according to the numerical tests and comparison with experimental data for a few cases related to ship hull sections with bilge keels

Active Control of a Non-Linear Ship model with External and Parametric Excitation

The response of a ship model with non-linearly coupled pitch and roll modes under modulated external and parametric solved and studied. The active control is applied to reduce the vibration of the system . The method of multiple scale perturbation technique is applied to obtain the periodic response equation near the primary resonance in the presence of internal resonance of the system. The objective of this research is focused on the stability of this periodic solution, dynamical properties and chaotic response. The stability of the obtained numerical solution is studied using both frequency response equation and phase-plane methods. The effects of some parameters on the vibrating system are investigated and reported in this paper

Approximate Super- and Sub-harmonic Response of a Multi-DOFs System with Local Cubic Nonlinearities under Resonance

A multi-degree-of-freedom dynamical system with local cubic nonlinearities subjected to super/subharmonic excitation is considered in this paper. The purpose of this paper is to approximate the nonlinear response of system at super/sub harmonic resonance. For many situations, single resonance mode is often observed to be leading as system enters into super/sub harmonic resonance. In this case, the single modal natural resonance theory can be applied to reduce the system model and a simplified model with only a single DOF is always obtained. Thus, an approximate solution and the analytical expression of frequency response relation are then derived using classical perturbation analysis. While the system is controlled by multiple modes, modal analysis for linearized system is used to decide dominant modes. The reduced model governed by these relevant modes is found and results in an approximate numerical solutions. An illustrative example of the discrete mass-spring-damper nonlinear vibration system with ten DOFs is examined. The approximation results are validated by comparing them with the calculations from direct numerical integration of the equation of motion of the original nonlinear system. Comparably good agreements are obtained