带弹性附件充液矩形贮箱俯仰运动动态响应
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摘要
首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响.
Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of the ideal fluid, the coupling dynamics equations of rigid tank, elastic appendages and liquid fuel were derived using H-O principle.In the case of pitch excitation,the modified potential function and wave height function were introduced to describe the moving boundary of fluid.Then Galerkin's method was used to discrete the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system were formulated in liquid depth, the length of the tank, and etc. The formulae are confirmed by numerical simulation,which also show the effect of liquid and elastic appendages on the attitude angular of rigid.
Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of the ideal fluid, the coupling dynamics equations of rigid tank, elastic appendages and liquid fuel were derived using H-O principle.In the case of pitch excitation,the modified potential function and wave height function were introduced to describe the moving boundary of fluid.Then Galerkin's method was used to discrete the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system were formulated in liquid depth, the length of the tank, and etc. The formulae are confirmed by numerical simulation,which also show the effect of liquid and elastic appendages on the attitude angular of rigid.
引文
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[4]Odd M Faltinsen,Olav F,Rognebakke,Ivan A Lukovsky,et al.Multidi mensional modal analysis of nonlinear sloshingin a rectangular tank withfinite water depth[J].J Fluid Mech,2000,407:201-234.
[5]Odd M Faltinsen,Alexander N Ti mokha.Asymptotic modal approxi mation of nonlinear resonant sloshing in a rectangular tank with small fluid depth[J].J Fluid Mech,2002,470,319-357.
[6]王照林,刘延柱.充液系统动力学[M].北京:科学出版社,2002.
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[15]岳宝增.俯仰激励下三维液体大幅晃动问题研究[J].力学学报,2005,37(2):199-203.
[16]李遇春,楼梦麟.渡槽中流体非线性晃动的边界元模拟[J].地震工程与工程振动,2000,20(2):51-56.
[17]李俊峰,王照林.带挠性伸展附件的航天器姿态动力学研究[J].清华大学学报,1996,36(10):35-40.
[18]Kalaycioglu S,Misra A K.Approxi mate silutions for vibration of deploying appendages[J].J Guid Cont Dyn,1991,14(2):287-293.
[19]贾英宏,徐世杰.充液挠性多体航天器的变结构控制[J].宇航学报,2002,23(3):18-23.
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[22]程绪铎,王照林,李俊峰.带弹性伸展附件充液航天器姿态动力学研究[J].空间科学学报,2000,20(3):271-277.
[2]Abramson H N.The dynamic behavior of liquids in moving containers[R].NASA SP106,1966.
[3]Odd MFaltinsen.A nonlinear theory of sloshingin rectangular tanks[J].Journal of Ship Research,1974,18(4):224-241.
[4]Odd M Faltinsen,Olav F,Rognebakke,Ivan A Lukovsky,et al.Multidi mensional modal analysis of nonlinear sloshingin a rectangular tank withfinite water depth[J].J Fluid Mech,2000,407:201-234.
[5]Odd M Faltinsen,Alexander N Ti mokha.Asymptotic modal approxi mation of nonlinear resonant sloshing in a rectangular tank with small fluid depth[J].J Fluid Mech,2002,470,319-357.
[6]王照林,刘延柱.充液系统动力学[M].北京:科学出版社,2002.
[7]尹立中.航天工程中液体大幅晃动及贮箱类液固耦合动力学研究[D].博士学位论文.哈尔滨:哈尔滨工业大学,1999.
[8]苟兴宇,尹立中,马兴瑞,等.窄长方形贮箱中液体的强迫晃动[J].力学与实践,1998,20(4):20-22.
[9]尹立中,刘敏,王本利,等.矩形贮箱类液固耦合系统的平动响应研究[J].振动工程学报,2000,13(3):433-437.
[10]马兴瑞,王本利,苟兴宇,等.航天动力学——若干问题进展及应用[M].北京:科学出版社,2001.
[11]陈科,李俊峰,王天舒.矩形贮箱内液体非线性晃动动力学建模与分析[J].力学学报,2005,37(3):339-344.
[12]曾江红.多腔充液自旋系统动力学与液体晃动三维非线性数值研究[D].博士论文.北京:清华大学工程力学系,1996.
[13]徐刚.大型薄壁结构与大晃动粘性流体的流固耦合数值研究[D].博士论文.北京:清华大学工程力学系,2003.
[14]岳宝增,刘延柱,王照林.三维液体非线性晃动动力学特性的数值模拟[J].应用力学学报,2001,18(1):110-115.
[15]岳宝增.俯仰激励下三维液体大幅晃动问题研究[J].力学学报,2005,37(2):199-203.
[16]李遇春,楼梦麟.渡槽中流体非线性晃动的边界元模拟[J].地震工程与工程振动,2000,20(2):51-56.
[17]李俊峰,王照林.带挠性伸展附件的航天器姿态动力学研究[J].清华大学学报,1996,36(10):35-40.
[18]Kalaycioglu S,Misra A K.Approxi mate silutions for vibration of deploying appendages[J].J Guid Cont Dyn,1991,14(2):287-293.
[19]贾英宏,徐世杰.充液挠性多体航天器的变结构控制[J].宇航学报,2002,23(3):18-23.
[20]贾英宏,徐世杰,荆武兴.带弹性附件的航天器的动力学与变结构控制[J].哈尔滨工业大学学报,2003,35(1):1-4.
[21]李铁成,王照林,李俊峰,等.刚-流-弹耦合系统动力方程及其动力边界条件的建立[J].应用力学学报,1998,15(2):127-131.
[22]程绪铎,王照林,李俊峰.带弹性伸展附件充液航天器姿态动力学研究[J].空间科学学报,2000,20(3):271-277.
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