Abstract: In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative.
Abstract: We propose a reduced-ordermodel for the instantaneous
hydrodynamic force on a cylinder. The model consists of a system of
two ordinary differential equations (ODEs), which can be integrated
in time to yield very accurate histories of the resultant force and
its direction. In contrast to several existing models, the proposed
model considers the actual (total) hydrodynamic force rather than its
perpendicular or parallel projection (the lift and drag), and captures
the complete force rather than the oscillatory part only. We study
and provide descriptions of the relationship between the model
parameters, evaluated utilizing results from numerical simulations,
and the Reynolds number so that the model can be used at any
arbitrary value within the considered range of 100 to 500 to provide
accurate representation of the force without the need to perform timeconsuming
simulations and solving the partial differential equations
(PDEs) governing the flow field.