| Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance |
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| 作者姓名： | LI Wei TANG You-gang LIU Li-qin LI Yan WANG Bin |
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| 作者单位： | State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China |
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| 基金项目： | This work was financially supported by the National Natural Science Foundation of China (Grant No. 51279130). |
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| 摘 要： | We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortex-induced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation.
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| 关 键 词： | spar platform three DOFs nonlinear equations multiple scales super-harmonic response energy infiltration |
| 收稿时间： | 2016/8/2 0:00:00 |
| 修稿时间： | 2016/12/2 0:00:00 |
Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance |
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| LI Wei,TANG You-gang,LIU Li-qin,LI Yan,WANG Bin.Internal Resonances for Heave, Roll and Pitch Modes of A Spar Platform Considering Wave and Vortex-Induced Loads in the Main Roll Resonance[J].Ocean Engineering,2017,31(4):408-417. |
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| Authors: | LI Wei TANG You-gang LIU Li-qin LI Yan and WANG Bin |
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| Institution: | State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China,State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China and State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University, Tianjin 300072, China;School of Civil Engineering, Tianjin University, Tianjin 300072, China;Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China |
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| Abstract: | We present a study of the nonlinear coupling internal resonance for the heave roll and pitch performance of a spar platform under the wave and vortex-induced loads when the ratio of the frequencies of heave, roll and pitch are approximately 2:1:1. In consideration of varying wet surface, the three DOFs nonlinear coupled equations are established for the spar platform under the effect of the first-order wave loads in the heave and pitch, and vortex-induced loads in the roll. By utilizing the method of multi-scales when the vortex-induced frequency is close to the natural roll frequency, the first-order perturbation solution is obtained analytically and further validated by the numerical integration. Sensitivity analysis is performed to understand the influence of the damping and the internal detuning parameter. Two cases with internal resonance are shown. The first case is that no saturation phenomenon exists under small vortex-induced loads. The first order perturbation solution illustrates that only the vortex-induced frequency motion in roll and the super-harmonic frequency motion in heave are excited. The second case is that the vortex-induced loads are large enough to excite the pitch and a saturation phenomenon in the heave mode follows. The results show that there is no steady response occurrence for some cases. For these cases chaos occurs and large amplitudes response can be induced by the vortex-induced excitation. |
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| Keywords: | spar platform three DOFs nonlinear equations multiple scales super-harmonic response energy infiltration |
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