# Two degree of freedom flow-induced vibration of cylindrical structures in marine environments: frequency ratio effects

## Abstract

The flow-induced vibration of a cylindrical structure is a very common problem in marine environments such as undersea pipelines, offshore risers, and cables. In this study, the vortex-induced vibration (VIV) of an elastically mounted cylinder at a low Reynolds number is simulated by a transient coupled fluid–structure interaction numerical model. Considering VIV with low damping ratio, the response, hydrodynamic forces, and vortex shedding modes of the cylinder is systematically analyzed and summed up the universal rule under different frequency ratios. On the basis of the analysis, we find that the frequency ratio α is a very important parameter. It decides the locked-in, beat, and phase-switch phenomena of the cylinder, meanwhile, it also influence the vortex mode of the cylinder. The trajectory of the two degrees of freedom (2 DOF) case at different natural frequency ratios is discussed, with most trajectories having a “figure of 8” shape and a few having a “crescent” shape. A fast Fourier transformation technique is used to obtain the frequency characteristics of the vibration of the cylindrical structure. Using the 2 DOF cylinder model in place of the 1 DOF model presents several advantages in simulating the nonlinear characteristics of cylindrical structures, including the capacity to model the crosswise vibration generated by in-line vibration.

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## Abbreviations

m* = m/m d :

Ratio of oscillating mass over displaced mass

ζ = δ/2π :

Damping ratio

$$f_{n} = \frac{1}{2\pi }\sqrt {\frac{k}{{m + m_{a} }}}$$ :

Natural frequency of elastic cylinder in still water

m a  = ρπD 2/4:

U * = U/(f n D):

Reduced velocity in water

f s :

Vortex shedding frequency of elastic cylinder

St = f 0 D/U :

Strouhal number in still water

Re = UD/ν :

Reynolds number

f 0 :

Vortex shedding frequency of fixed cylinder

α = f n /f 0 :

Frequency ratio

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## Acknowledgments

This study was supported by a guiding fund for the integration of industry, education and research of Guangdong Province, China (Grant No. 2012B091100132), a middle-aged and young teachers’ basic ability promotion project of Guangxi Zhuang Autonomous Region (Numerical simulation research of marine riser vortex-induced vibration), the key discipline of guangxi colleges and universities - automation and machinery manufacturing.

## Author information

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### Corresponding authors

Correspondence to Youhong Tang or Chengbi Zhao.

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