Abstract
In marine engineering, the dynamics of fixed offshore structures (for oil and gas production or for wind turbines) are normally found by modelling of the motion by a classical mass-spring damped system. On slender offshore structures, the loading due to waves is normally calculated by applying a force which consists of two parts: a linear “inertia/mass force” and a non-linear “drag force” that is proportional to the square of the velocity of the particles in the wave, multiplied by the direction of the wave particle motion. This is the so-called Morison load model. The loading function can be expanded in a Fourier series, and the drag force contribution exhibits higher order harmonic loading terms, potentially in resonance with the natural frequencies of the system. Currents are implemented as constant velocity terms in the loading function. The paper highlights the motion of structures due to non-linear resonant motion in an offshore environment with high wave intensity. It is shown that “burst”/“ringing” type motions could be triggered by the drag force during resonance situations.
Highlights
The irregular wave environment is normally modelled as a linear sum of sinusoidal waves, using a Fourier representation of the actual wave environment
In [13], we investigated drag forcing can act as of a damping structural displacement, and the drag loading term is proportional to the wave water term in the system, and whether it could act as negative damping, enhancing the velocity squared
Limit cycles represent the solution of a linear second order ordinary differential equation subject to non-linear drag loading
Summary
The irregular wave environment is normally modelled as a linear sum of sinusoidal waves, using a Fourier representation of the actual wave environment. As it is of particular interest to study the response (x is the displacement of the structure as a function of time) to non-linear load effects (as these can give rise to higher order non-linear resonances [12]), a one degree of freedom system with a non-linear drag loading term of the Morison type, caused by a wave having a frequency, ω, could be reformulated as: d2 x dx m 2 +c. It should be noted that the response of a structure is often calculated in the time domain given the wave profile; analytical studies, like the study presented help to identify specific aspects of the solution, like the large non-linear resonances: the “burst”/“ringing” effect reported in this paper. The drag and inertia coefficients should be given as functions of the water wave kinematics; often these coefficients are taken as constants over the water depth and over the wave field, as the main contributions to the loading come from near-surface effects in the largest waves [11]
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