弹性地基上矩形贮液结构的液-固耦合振动特性
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摘要
针对无旋、无粘和不可压缩的理想液体,根据Winkler弹性地基上矩形贮液结构的液-固耦合振动分析模型,通过引入无量纲参数建立了矩形贮液结构的液-固耦合系统的振动方程。为简化计算,根据梁的振型函数和频率方程,将三维问题转化为一维问题来处理,利用振型函数的正交性求解了Winkler弹性地基上矩形贮液结构的液-固耦合振动频率。最后,为便于工程应用,结合工程实际讨论了无量纲参数对矩形贮液结构液-固耦合振动频率的影响,从而为以后工程结构中矩形贮液结构的设计计算提供了理论依据。
In connection with the irrotational,inviscid and incompressible ideal liquid,and according to a liquid-solid coupling vibration analysis model of rectangular liquid-storage structures on a Winkler elastic foundation,the vibration equation of rectangular liquid-storage structures considering liquid-solid coupling is established by introducing dimensionless parameters.In order to simplify the calculation,the three-dimension problem is transformed into the one-dimension by the mode shape function and frequency equation of a beam.The liquid-solid coupling vibration frequency of rectangular liquid storage structures on the Winkler elastic foundation is obtained through using the orthogonality of vibration mode functions.Finally,for the convenience of engineering application,the influence of dimensionless parameters on the liquid-solid coupling vibration frequency of rectangular liquid-storage structures is discussed considering engineering practice.Thusly,the theory base about the design calculation of the rectangular liquid-storage structures is provided for corresponding engineering structures.
In connection with the irrotational,inviscid and incompressible ideal liquid,and according to a liquid-solid coupling vibration analysis model of rectangular liquid-storage structures on a Winkler elastic foundation,the vibration equation of rectangular liquid-storage structures considering liquid-solid coupling is established by introducing dimensionless parameters.In order to simplify the calculation,the three-dimension problem is transformed into the one-dimension by the mode shape function and frequency equation of a beam.The liquid-solid coupling vibration frequency of rectangular liquid storage structures on the Winkler elastic foundation is obtained through using the orthogonality of vibration mode functions.Finally,for the convenience of engineering application,the influence of dimensionless parameters on the liquid-solid coupling vibration frequency of rectangular liquid-storage structures is discussed considering engineering practice.Thusly,the theory base about the design calculation of the rectangular liquid-storage structures is provided for corresponding engineering structures.
引文
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[15]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983:1―9.Ju Rongchu,Zeng Xinchuan.Vibration theory of elastic structure coupled with the liquid[M].Beijing:Earthquake Press,1983:1―9.(in Chinese)
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[17]莫乃榕.工程流体力学[M].武汉:华中科技大学出版社,2003:7―10.Mo Nairong.Engineering fluid dynamics[M].Wuhan:Huazhong University of Science and Technology Press,2003:7―10.(in Chinese)
[18]Werner P W,Sundquist K J.On hydrodynamic earthquake effects[J].Transaction of the American Geophysical Union,1949,30(5):636―657.
[19]杜永峰,史晓宇,程选生.钢筋混凝土矩形贮液结构的液-固耦合动力分析[J].西北地震学报,2008,30(1):21―26.Du Yongfeng,Shi Xiaoyu,Cheng Xuansheng.Dynamic analysis of reinforced concrete rectangular liquid storage structures considering liquid-structure interaction[J].Northwestern Seismological Journal,2008,30(1):21―26.(in Chinese)
[20]高淑英,沈火明.线性振动教程[M].北京:中国铁道出版社,2003:131―135.Gao Shuying,Shen Huoming.Linear vibration course[M].Beijing:China Railway Publishing House,2003:131―135.(in Chinese)
[21]郭天木.水池底板对池壁的嵌固条件[J].特种结构,1998,15(4):1―4.Guo Tianmu.Restraining condition of cistern base plate to wall[J].Special Structures,1998,15(4):1―4.(in Chinese)
[2]王照林,程绪铎,金斌.微重状态下带有隔板的球形贮箱内液体晃动特性的研究[J].空间科学学报,1990,10(2):107―119.Wang Zhaolin,Cheng Xuduo,Jin Bin.Liquid sloshing in spherical tank with spacer at low gravity environment[J].Chinese Journal of Space Science,1990,10(2):107―119.(in Chinese)
[3]Choun Young-sun,Yun Chung-bang.Sloshing characteristics in rectangular tanks with a submerged block[J].Computers&Structures,1996,61(3):401―413.
[4]Ikeda T,Nakagawa N.Non-linear vibrations of a structure caused by water sloshing in a rectangular tank[J].Journal of Sound and Vibration,1997,201(1):23―41.
[5]Warnitchai P,Pinkaew T.Modelling of liquid sloshing in rectangular tanks with flow-dampening devices[J].Engineering Structures,1998,20(7):593―600.
[6]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―345.Chen Ke,Li Junfeng,Wang Tianshu.Dynamic modeling and analysis of liquid non-liner sloshing in rectangular tanks[J].Chinese Journal of Theoretical and Applied Mechanics,2005,37(3):339―345.(in Chinese)
[7]岳宝增,王照林,李俊峰.带有弹性隔板的圆柱形贮箱内液体的晃动问题[J].清华大学学报,1997,37(8):26―28.Yue Baozeng,Wang Zhaolin,LI Junfeng.The questions of liquid sloshing in a cylindrical tank with elastic spacer[J].Journal of Tsinghua University,1997,37(8):26―28.(in Chinese)
[8]程绪铎,王照林.带弹性隔板的矩形贮箱中流弹耦合振动问题[J].力学与实践,1999,21(6):50―52.Cheng Xuduo,Wang Zhaolin.Hydroelastic vibrations rectangular tank with elastic spacer[J].Mechanics in Engineering,1999,21(6):50―52.(in Chinese)
[9]张素侠,刘习军,贾芬.矩形弹性壳液耦合系统的模态试验分析[J].机械强度,2004,26(6):615―619.Zhang Suxia,Liu Xijun,Jia Fen.Modal test of elastic rectangular shell coupling system[J].Journal of Mechanical Strength,2004,26(6):615―619.(in Chinese)
[10]刘习军,张素侠,刘国英.矩形弹性壳液耦合系统中的重力波分析[J].力学学报,2006,38(1):106―112.Liu Xijun,Zhang Suxia,Liu Guoying.Gravity waves analysis of elastic rectangular shell coupling system[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(1):106―112.(in Chinese)
[11]傅衣铭,徐晓贤.弹性底板矩形贮箱流固耦合系统的自由振动分析[J].湖南大学学报(自然科学版),2006,33(1):33―37.Fu Yiming,Xu Xiaoxian.Analysis about free vibration of rectangular tank the liquid-solid coupling system with elastic soleplate[J].Journal of Hunan University(Natural Sciences),2006,33(1):33―37.(in Chinese)
[12]程选生.钢筋混凝土矩形贮液结构的热力学性能及液-固耦联振动[D].兰州:兰州理工大学,2007.Cheng Xuansheng.Energetics performance and liquid-structure interaction vibration of reinforced concrete rectangular fluid-tank[D].Lanzhou:Lanzhou University of Technology,2007.(in Chinese)
[13]上海市政工程设计院.给水排水工程结构设计手册[M].北京:中国建筑工业出版社,1984:1474―1477.Shanghai City Planning Engineering Designing Institute.Feedwater and drainage engineering designing handbook[M].Beijing:China Construction Industry Press,1984:1477―1477.(in Chinese)
[14]刘健行,郭先瑚,苏景春.给水排水工程结构[M].北京:中国建筑工业出版社,2006:295―344.Liu Jianhang,Guo Xianhu,Su Jingchun.Feed water and drainage engineering structure[M].Beijing:China Architecture&building Press,2006:295―344.(in Chinese)
[15]居荣初,曾心传.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983:1―9.Ju Rongchu,Zeng Xinchuan.Vibration theory of elastic structure coupled with the liquid[M].Beijing:Earthquake Press,1983:1―9.(in Chinese)
[16]董曾南,章梓雄.非粘性流体力学[M].北京:清华大学出版社,2003.Dong Zengnan,Zhang Zixiong.Non-viscous fluid dynamics[M].Beijing:Tsinghua University Press,2003.(in Chinese)
[17]莫乃榕.工程流体力学[M].武汉:华中科技大学出版社,2003:7―10.Mo Nairong.Engineering fluid dynamics[M].Wuhan:Huazhong University of Science and Technology Press,2003:7―10.(in Chinese)
[18]Werner P W,Sundquist K J.On hydrodynamic earthquake effects[J].Transaction of the American Geophysical Union,1949,30(5):636―657.
[19]杜永峰,史晓宇,程选生.钢筋混凝土矩形贮液结构的液-固耦合动力分析[J].西北地震学报,2008,30(1):21―26.Du Yongfeng,Shi Xiaoyu,Cheng Xuansheng.Dynamic analysis of reinforced concrete rectangular liquid storage structures considering liquid-structure interaction[J].Northwestern Seismological Journal,2008,30(1):21―26.(in Chinese)
[20]高淑英,沈火明.线性振动教程[M].北京:中国铁道出版社,2003:131―135.Gao Shuying,Shen Huoming.Linear vibration course[M].Beijing:China Railway Publishing House,2003:131―135.(in Chinese)
[21]郭天木.水池底板对池壁的嵌固条件[J].特种结构,1998,15(4):1―4.Guo Tianmu.Restraining condition of cistern base plate to wall[J].Special Structures,1998,15(4):1―4.(in Chinese)
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