平动矩形贮箱刚-液耦合非线性动力学研究
|
摘要
首先应用H-O原理建立了矩形贮箱刚-液耦合系统平动的耦合动力学模型,在贮箱水平运动情况下,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,在给定贮箱运动规律和给定外力规律两种形式下,分析了刚-液耦合系统固有频率变化规律,并应用多尺度法对系统的一阶主共振进行解析分析,研究了液体稳态解的幅频曲线,均发现跳跃及软、硬特性随液深转换的现象,在给定水平外力下,得到液体稳态解的同时还可得到刚体稳态解,两者定性性态相同。最后用数值法验证了解析解的正确性。
Based on ideal fluid assumption, the coupling dynamic equations of rigid tank and nonlinear sloshing of liquid are established through H-O principle with surface tension and damping considered. The modified potential function and wave height function are introduced to describe the moving boundary of fluid and rigid tank which is forced in surge. Galerkin’s method is used to discrete the dynamics equations into ordinary differential equations. Both the movement and the motivation of rigid tank are considered. The natural frequencies of the rigid-liquid coupling system are formulated with liquid depth, the length of the tank, and etc. The nonlinear dynamics of the rigid-liquid coupling system is investigated analytically. Using the multi-scale method, the amplitude-frequency response is obtained and the jumping phenomenon is observed. It is also observed that as the depth of liquid decreases, the soft and hard characteristics transform to each other. Subsequently, the effects of all factors are studied in detail. Under the condition of giving horizontal excitation, we also can analyze the stable solution of the rigid, which is the same as liquid in qualitative analysis. Finally, compared to the numerical solution, the analytic solution proves to be feasible.
Based on ideal fluid assumption, the coupling dynamic equations of rigid tank and nonlinear sloshing of liquid are established through H-O principle with surface tension and damping considered. The modified potential function and wave height function are introduced to describe the moving boundary of fluid and rigid tank which is forced in surge. Galerkin’s method is used to discrete the dynamics equations into ordinary differential equations. Both the movement and the motivation of rigid tank are considered. The natural frequencies of the rigid-liquid coupling system are formulated with liquid depth, the length of the tank, and etc. The nonlinear dynamics of the rigid-liquid coupling system is investigated analytically. Using the multi-scale method, the amplitude-frequency response is obtained and the jumping phenomenon is observed. It is also observed that as the depth of liquid decreases, the soft and hard characteristics transform to each other. Subsequently, the effects of all factors are studied in detail. Under the condition of giving horizontal excitation, we also can analyze the stable solution of the rigid, which is the same as liquid in qualitative analysis. Finally, compared to the numerical solution, the analytic solution proves to be feasible.
引文
[1]莫依舍夫H H,鲁面采夫B B.充液刚体动力学[M].韩子鹏译.北京:宇航出版社,1992.Moiseev N N,Rumyantesev V V.Dynamics of liquid-filled rigid body[M].Beijing:Aerospace Press,1992.(in Chinese)
[2]Abramson H N.The dynamic behavior of liquids in moving containers[R].NASA:SP106,1966.
[3]Odd M Faltinsen.A nonlinear theory of sloshing in rectangular tanks[J].Journal of Ship Research,1974,18(4):224~241.
[4]马兴瑞.航天动力学——若干问题进展及应用[M].北京:科学出版社,2001.Ma Xingrui.Dynamics of spacecraft—developments and applications of some problems[M].Beijing:Science Press,2001.(in Chinese)
[5]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].哈尔滨:哈尔滨工业大学,1999.Yin Lizhong.Study on large sloshing of liquid and dynamics of liquid-solid coupling systems[D].Harbin:Harbin Institute of Technology,1999.(in Chinese)
[6]Odd M Faltinsen,Olav F Rognebakke,Ivan A Lukovsky,Alexander N Timokha.Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth[J].J.Fluid Mech.,2000,407:201~234.
[7]Odd M Faltinsen,Alexander N Timokha.Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth[J].J.Fluid Mech.,2002,470:319~357.
[8]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.Chen Ke,Li Junfeng,Wang Tianshu.Nonlinear dynamics modeling and analysis of liquid sloshing in rectangular tanks[J].Acta Mechanica Sinica,2005,37(3):339~344.(in Chinese)
[9]王照林,刘延柱.充液系统动力学[M].北京:科学出版社,2002.Wang Zhaolin,Liu Yanzhu.Dynamics of liquid-filled systems[M].Beijing:Science Press,2002.(in Chinese)
[10]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].北京:清华大学工程力学系,1996.Zeng Jianghong.Dynamics of spinning system with partially liquid-filled tanks and numerical study of three-dimensional nonlinear liquid sloshing[D].Beijing:Tsinghua University,1996.(in Chinese)
[11]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].北京:清华大学工程力学系,2003.Xu Gang.Numerical study on fluid-structure interaction between large-scale thin-walled structures and viscous fluid with large sloshing[D].Beijing:Tsinghua University,2003.(in Chinese)
[12]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.Yue Baozeng,Liu Yanzhu,Wang Zhaolin.ALE finite element method for three-dimensional large amplitude liquid sloshing using fractional step method[J].Chinese Journal of Applied Mechanics,2001,18(1):110~115.(in Chinese)
[13]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.Yue Baozeng.Three-dimensional large amplitude liquid sloshing under pitching excitation[J].Acta Mechanica Sinica,2005,37(2):199~203.(in Chinese)
[14]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.Li Yuchun,Lou Menglin.BEM simulation of nonlinear sloshing for aqueduct fluid[J].Earthquake Engineering and Engineering Vibration,2000,20(2):51~56.(in Chinese)
[2]Abramson H N.The dynamic behavior of liquids in moving containers[R].NASA:SP106,1966.
[3]Odd M Faltinsen.A nonlinear theory of sloshing in rectangular tanks[J].Journal of Ship Research,1974,18(4):224~241.
[4]马兴瑞.航天动力学——若干问题进展及应用[M].北京:科学出版社,2001.Ma Xingrui.Dynamics of spacecraft—developments and applications of some problems[M].Beijing:Science Press,2001.(in Chinese)
[5]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].哈尔滨:哈尔滨工业大学,1999.Yin Lizhong.Study on large sloshing of liquid and dynamics of liquid-solid coupling systems[D].Harbin:Harbin Institute of Technology,1999.(in Chinese)
[6]Odd M Faltinsen,Olav F Rognebakke,Ivan A Lukovsky,Alexander N Timokha.Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth[J].J.Fluid Mech.,2000,407:201~234.
[7]Odd M Faltinsen,Alexander N Timokha.Asymptotic modal approximation of nonlinear resonant sloshing in a rectangular tank with small fluid depth[J].J.Fluid Mech.,2002,470:319~357.
[8]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.Chen Ke,Li Junfeng,Wang Tianshu.Nonlinear dynamics modeling and analysis of liquid sloshing in rectangular tanks[J].Acta Mechanica Sinica,2005,37(3):339~344.(in Chinese)
[9]王照林,刘延柱.充液系统动力学[M].北京:科学出版社,2002.Wang Zhaolin,Liu Yanzhu.Dynamics of liquid-filled systems[M].Beijing:Science Press,2002.(in Chinese)
[10]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].北京:清华大学工程力学系,1996.Zeng Jianghong.Dynamics of spinning system with partially liquid-filled tanks and numerical study of three-dimensional nonlinear liquid sloshing[D].Beijing:Tsinghua University,1996.(in Chinese)
[11]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].北京:清华大学工程力学系,2003.Xu Gang.Numerical study on fluid-structure interaction between large-scale thin-walled structures and viscous fluid with large sloshing[D].Beijing:Tsinghua University,2003.(in Chinese)
[12]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.Yue Baozeng,Liu Yanzhu,Wang Zhaolin.ALE finite element method for three-dimensional large amplitude liquid sloshing using fractional step method[J].Chinese Journal of Applied Mechanics,2001,18(1):110~115.(in Chinese)
[13]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.Yue Baozeng.Three-dimensional large amplitude liquid sloshing under pitching excitation[J].Acta Mechanica Sinica,2005,37(2):199~203.(in Chinese)
[14]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.Li Yuchun,Lou Menglin.BEM simulation of nonlinear sloshing for aqueduct fluid[J].Earthquake Engineering and Engineering Vibration,2000,20(2):51~56.(in Chinese)
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心