Power flow analysis of an equipment-nonlinear isolator-flexible ship interaction system excited by progressive sea waves

Abstract

A Power Flow Analysis or a Statistical Energy Analysis provides a powerful approach to model the dynamical behaviour of various complex coupled systems. While significant non-linear behavior has been observed in many vibration isolation systems, most studies are typically based on the concept of linear theory in terms of force or motion transmissibility. In this paper, a non-linear isolation system mounted on a flexible beam-like ship travelling on a seaway is investigated from a vibratory power flow viewpoint. A mathematical model describing a ship-equipment dynamical interaction system excited by sea waves is presented. The ship is modelled as a uniform beam floating on the surface of water and equipment is mounted on the beam-like ship through a nonlinear spring and damper. It is assumed that the water surface has a sinusoidal disturbance ξ(x,t) = asin(kx-ωet), which excites the ship with frequency of encounter ωe and wavelength 2π/k. This wave system produces fluid actions involving inertial, damping and buoyancy forces and the interacting ship-wave system is treated as a nonlinear dynamical coupled system. The nonlinear functions in the stiffness and damping are approximated by Fourier expansions up to first order and a harmonic balance technique is used to obtain the dynamic responses of the system. The non-linear system is analysed by using a power flow approach. The power flow input to the system by the seawaves, the absorbed power by the non-linear isolator and the vibratory power transmitted to the equipment are presented. Nonlinear power flow phenomena and the effects of nonlinear parameters on power flow transmission spectra are discussed and examined. Valuable information and guidelines are derived to achieve an effective vibration isolation design system applicable to ship operations and to other applications in maritime engineering so as to eliminate vibrations and to protect equipment in a sea environment.

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ORCID for Y.P. Xiong: orcid.org/0000-0002-0135-8464

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