Vibration Control for a Coupled Pitch- roll Ship Model Via a Negative Cubic Velocity Feedback Control

One of the most essential ship reactions to waves is roll motion. Due to the intricacy of ship wave interactions and their sensitivity, predicting such a reaction is extremely challenging. Because vibration motion is an undesirable occurrence, it must be removed, decreased, or controlled. A coupled Pitch- roll ship model with negative cubic velocity feedback control subjected to parametric excitations is premeditated and solved in this paper. The method of multiple time scales is applied to scrutinize the response of the two modes of the system neighbouring the simultaneous sub-harmonic, and internal resonance situation. Besides, the steady-state solution is determined through the Rung-Kutta Method (RKM) of fourth order. Stability of the steady state solution near this resonance case is discussed and studied applying Lyapunov’s first indirect method and Routh- Hurwitz criterion. The influences of the different parameters on the steady state solution are reconnoitred and discussed. The controller effects on the stability are clarified. Simulation results are accomplished with the help of MATLAB and Maple software programs

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

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

Stability and local bifurcation analysis for a nonlinear coupled helicopter blade-absorber system via normal form method

Consider the effect of nonlinear spring and linear viscous damping in structure, the motion equations of a helicopter blade-absorber system has been established by Lagrange equation. Since the helicopter blade-absorber system exists motion coupling, the inertia and stiffness terms of equations are decoupled via equivalent principal coordinate transformation. The stability and local bifurcation behaviors of the principal coordinate equations are investigated with the aid of multiple scales method and normal form theory. Two kinds of critical points for the bifurcation response equations near the combination resonance are considered, which are characterized by a pair of purely imaginary eigenvalues and double zero eigenvalues. The Hopf bifurcation solution, bifurcation path, and transition curves of the model are investigated respectively. For each case, the numerical results obtained by Runge-Kutta method coincide with the analytical predictions. These results may provide some guidance for parameter design of helicopter blade-absorber system

Steady State and Transient Dynamical Systems Analysis of Uncoupled Roll Response for a Traditional Versus Advanced Hull Form

The two ships represented in this thesis are dramatically different in design, but both exhibit similar properties such as length and breadth. The traditional hull form is represented by a typical flare-sided design with a forward reaching bow while the advanced hull form has a modified tumblehome and a truncated bow. The difference in shapes provides an interesting problem, comparing the roll responses for these two very different vessels while keeping certain shape parameters such as length, beam, and draft constant

Steady State and Transient Dynamical Systems Analysis of Uncoupled Roll Response for a Traditional Versus Advanced Hull Form

The two ships represented in this thesis are dramatically different in design, but both exhibit similar properties such as length and breadth. The traditional hull form is represented by a typical flare-sided design with a forward reaching bow while the advanced hull form has a modified tumblehome and a truncated bow. The difference in shapes provides an interesting problem, comparing the roll responses for these two very different vessels while keeping certain shape parameters such as length, beam, and draft constant