| Riser is a kind of pipeline equipment in the field of ocean engineering,which is very important in the production and operations in ocean engineering.Vortex-induced vibration(VIV)is an important cause of fatigue damage about risers.Risers are generally slender cylindrical structures,and researchers often regard the study of VIV of rigid cylinders as the basis for predicting the VIV of risers.At present,the study on the prediction of VIV is mainly focused on the cross-flow vibration with large amplitude.However,lots of experiments on VIV show that the coupling effect of the in-line vibration on the transverse vibration can not be ignored.And the frequency of in-line vibration is higher,which has a great influence on the fatigue damage.The model prediction accuracy of the VIV with two degrees of freedom(DOF)still needs to be improved.Therefore,we present a new type of high order nonlinear oscillator model used to predict the VIV characteristics of low mass ratio of cylinders with two DOF.And by combining the above method,we also present a nonlinear oscillator model which can qualitatively and quantitatively predicte the VIV amplitude characteristics of two side-by-side cylinders.The main work of this paper is as follows:Firstly,the vibration equation of a cylinder fixed elastically by four springs is derived based on the Lagrange second dynamic equation,and then it is simplified by using Taylor function expansion formula.The items will be ignored if they are above three steps,and then the nonlinear structural vibration equation is obtained.Because the axial tensile and coupling nonlinearities are considered,this equation is helpful to improve the accuracy of calculation.Based on the discrete point vortex theory,the fluctuating lift and f drag are derived,and the mathematical relations between them are obtained.The angle problem caused by the relative velocity between the flow and the cylinder is considered.The high order improvement of the classical Van der Pol equation is conducted to simulate the high amplitude of the cylinder with low mass ratio.The coupled higher order nonlinear oscillator model is obtained by combining the nonlinear vibration equation and the higher order Van der Pol equation.Secondly,the prediction of a rigid cylinder with two DOF VIV is carried out by using high order nonlinear oscillator model.The in-line and cross-flow amplitude,Dimensionless characteristics of frequency as well as trajectory are found to be in agreement with the experimental results.Then the changes of amplitude characteristics are analysed in different mass ratio and damping ratio.On this basis,the sensitivity analyses of the geometric nonlinear parameters,coupling parameters and damping parameters of the fluid oscillator are carried out.Thirdly,the vibration equation of two side-by-side cylinders fixed by seven springs is derived based on the Lagrange second dynamic equation.Because of the large number of springs,only the linear term is considered for the purpose of simplification.By combining the derivation of the fluid force and the improved Van der Pol equation,the nonlinear vibration model for predicting the VIV characteristics of the side-by-side cylinders is proposed.The coupled equation is solved in in the column with a spacing ratio of 2.6,and the results are copared with experimental data to verify the correctness of the model.Meanwhile,the effects of the spacing ratio on VIV characteristics of the side-by-side cylinders are discussed based on the results of the model predictions and the experimental results,and the Correctness and applicability are verified again.In a word,based on the Lagrange second dynamic equation,discrete vortex theory and Van der Pol equation,two kinds of nonlinear oscillator models are proposed to predict the VIV of single cylinder and side-by-side cylinders.And the predictions are satisfying.The research has a practical significance in engineering,and can be used as a reference for the VIV of the risers. |
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