Interactive power flow characteristics of an integrated equipment—nonlinear isolator—travelling flexible ship excited by sea waves

A nonlinear interactive system comprising of equipment, nonlinear isolator and travelling flexible ship excited by waves is studied from a vibratory power flow viewpoint to examine its dynamical behaviour and power flow characteristics. The mathematical model describing the dynamics of this nonlinear interactive system is developed. Dynamical interactions between equipment, nonlinear isolator, flexible foundation and water waves are addressed. The nonlinearities of the isolator are characterized by a general pth power model for damping and qth power for stiffness. A harmonic balance method is adopted to derive the steady-state harmonic response of the nonlinear system. A Newton–Raphson iteration process in association with an efficient numerical algorithm is used to obtain the solutions of this nonlinear problem. Through simulations the dynamical behaviour, power flow characteristics and isolation efficiency of this complex nonlinear interaction system are investigated. For different values of power p and q, different wave excitations and flexible or rigid ship, the power transmitted to the equipment and power flow transmission ratios are calculated and analysed. The effect of the vibration source with different wave conditions of the seaway is studied through examining its vibratory power input to the overall system. The effects of the assumptions of flexible or rigid ship, the nonlinearities on the power flows in the system are examined. Nonlinear power flow phenomena and mechanisms are revealed, which provides an insight to the understanding of power flow characteristics in nonlinear systems. Practical guidelines for the design of vibration isolation systems applicable to maritime engineering are suggested.