变张力传递矩阵法在海洋立管模态分析中的应用
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摘要
矩阵传递法是解决梁结构弯曲振动的有效方法。基于经典传递矩阵法,将海洋立管离散成一系列集中质量和弹性梁单元,可建立一种快速计算海洋立管模态参数(固有频率及模态振型)的方法。通过计算发现,当总传递矩阵行列式值为0时,迭代频率即为立管的固有频率,基于此可求立管的模态振型。适当增加立管的离散单元数可使其固有频率值满足精度的要求。对立管轴向变张力和恒张力这两种情况下的模态进行了比较,发现由表观重力和管内外压差引起的轴向变张力对海洋立管的模态响应有一定的影响,立管的模态位移幅值比恒张力情况下的偏低一些。
Transfer matrix method(TMM)is an effective technique to solve the problem of beam bending vibration.By discretizing the riser into a series of lumped mass and beam elements, an approach to extracting modal characteristics(natural frequency and mode shape) has been developed based on the TMM. Natural frequencies can be determined when the determinant of the total transfer matrix is equal to zero. Then mode shape of the riser can be obtained. Accuracy of the calculation can be improved by increasing discrete elements. It is found that the axial tension and displacement amplitude of the riser with variable tension is lower than that of the riser with constant tension.
Transfer matrix method(TMM)is an effective technique to solve the problem of beam bending vibration.By discretizing the riser into a series of lumped mass and beam elements, an approach to extracting modal characteristics(natural frequency and mode shape) has been developed based on the TMM. Natural frequencies can be determined when the determinant of the total transfer matrix is equal to zero. Then mode shape of the riser can be obtained. Accuracy of the calculation can be improved by increasing discrete elements. It is found that the axial tension and displacement amplitude of the riser with variable tension is lower than that of the riser with constant tension.
引文
[1]张国进.海洋立管设计准则研究[D].杭州:浙江工业大学,2017.
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[7]季文美,方同,陈松淇.机械振动[M].北京:科学出版社,1985.
[8]CHEN Dongyang,ABBAS L K,RUI Xiaoting,et al.Dynamic modeling of sail mounted hydroplanes system-Part I:Modal characteristics from a transfer matrix method[J].Ocean Engineering,2017,130(15):629-644.
[9]KANG H J,XIE Weidong,GUO Tingdong.Modeling and parametric analysis of arch bridge with transfer matrix method[J].Applied Mathematical Modelling.2016,40(23-24):10578-10595.
[10]张宇峰,张广明,邓歆.基于传递矩阵法的磁轴承转子振动特性分析[J].电机与控制应用,2017,44(3):71-77.
[11]周维星,姚熊亮,傅晓军,等.舰艇管路抗冲击分析的传递矩阵法[J].结构力学.2014,10:1244-1253.
[12]王琳,李玉星,刘昶,等.考虑弹性基础的气液两相流海洋立管耦合振动分析[J].中国石油大学学报:自然科学版.2016,40(1):134-139.
[13]DAREING D W,HUANG T.Natural frequencies of marine drilling risers[J].Journal of Petroleum Technology,1976,28(7):813-818.
[14]HUANG Chaojun,SUN Peng,NAGARAJAIAH S,et al.Time-frequency methods for structural health monitoring of deepwater risers subjected to vortex induced vibrations[C]//Proceedings of the SPIE,2013,8692:86923E-2.
[15]ZHOU Xingkun,DUAN Menglan,GRANADOS J J.Precise integration method for natural frequencies and mode shapes of ocean risers with elastic boundary conditions[J].Applied Mathematical Modelling,2018,61:709-725.
[16]KANG H J,XIE Weidong,GUO Tingdong.Modeling and parametric analysis of arch bridge with transfer matrix method[J].Applied Mathematical Modelling,2016,40(23-24):10578-10595.
[17]DANESHFARAZ R,KAYA B.Solution of the propagation of the waves in open channels by the transfer matrix method[J].Ocean Engineering,2008,35(2008):1075-1079.
[18]LEE J W,LEE J Y.Free vibration analysis using the transfer-matrix method on a tapered beam[J].Computers and Structures,2016,164(2016):75-82.
[2]雷松,郑向远,张文首,等.海洋立管悬挂状态的固有频率和振型[J].船舶力学,2015,19(10):1267-1274.
[3]雷松,张文首,林家浩,等.海洋立管的模态及参数敏感性分析[J].船海工程,2012,41(4):136-141.
[4]LIE H,KAASEN K E.Modal analysis of measurements from a large-scale VIV model test of a riser in linearly sheared flow[J].Journal of Fluids and Structures,2006,22(4):557-575.
[5]ZHOU Xingkun,WANG Dongshi,DUAN Menglan,et al.Numerical study on mode curvature for damage detection of a drilling riser using transfer matrix technique[J].Applied Ocean Research,2017,63(2017):65-75.
[6]宋永奇,王永顺,丁静,等.模态分析和仿真技术与状态监测在海洋平台设备故障中的应用[J].北京石油化工学院学报.2015(1):45-48.
[7]季文美,方同,陈松淇.机械振动[M].北京:科学出版社,1985.
[8]CHEN Dongyang,ABBAS L K,RUI Xiaoting,et al.Dynamic modeling of sail mounted hydroplanes system-Part I:Modal characteristics from a transfer matrix method[J].Ocean Engineering,2017,130(15):629-644.
[9]KANG H J,XIE Weidong,GUO Tingdong.Modeling and parametric analysis of arch bridge with transfer matrix method[J].Applied Mathematical Modelling.2016,40(23-24):10578-10595.
[10]张宇峰,张广明,邓歆.基于传递矩阵法的磁轴承转子振动特性分析[J].电机与控制应用,2017,44(3):71-77.
[11]周维星,姚熊亮,傅晓军,等.舰艇管路抗冲击分析的传递矩阵法[J].结构力学.2014,10:1244-1253.
[12]王琳,李玉星,刘昶,等.考虑弹性基础的气液两相流海洋立管耦合振动分析[J].中国石油大学学报:自然科学版.2016,40(1):134-139.
[13]DAREING D W,HUANG T.Natural frequencies of marine drilling risers[J].Journal of Petroleum Technology,1976,28(7):813-818.
[14]HUANG Chaojun,SUN Peng,NAGARAJAIAH S,et al.Time-frequency methods for structural health monitoring of deepwater risers subjected to vortex induced vibrations[C]//Proceedings of the SPIE,2013,8692:86923E-2.
[15]ZHOU Xingkun,DUAN Menglan,GRANADOS J J.Precise integration method for natural frequencies and mode shapes of ocean risers with elastic boundary conditions[J].Applied Mathematical Modelling,2018,61:709-725.
[16]KANG H J,XIE Weidong,GUO Tingdong.Modeling and parametric analysis of arch bridge with transfer matrix method[J].Applied Mathematical Modelling,2016,40(23-24):10578-10595.
[17]DANESHFARAZ R,KAYA B.Solution of the propagation of the waves in open channels by the transfer matrix method[J].Ocean Engineering,2008,35(2008):1075-1079.
[18]LEE J W,LEE J Y.Free vibration analysis using the transfer-matrix method on a tapered beam[J].Computers and Structures,2016,164(2016):75-82.