柔性贮箱内液体晃动的分析模型
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摘要
研究了贮箱内液体晃动建模中贮箱的柔性与刚性、液体自由面的晃动与非晃动之间的差别.利用液体晃动特征模态和容器结构振动特征模态将液体晃动和弹性结构振动这2个相互耦合的微分方程边值问题进行离散,从而导出了液固耦合系统的动力学方程、相应的液固耦合系统固有频率方程以及液体晃动对容器和充液容器系统对基座的作用力主矢主矩的计算表达式.通过数值计算,比较了刚性贮箱和柔性贮箱之间在液体晃动频率和晃动作用力主矢主矩上的差异;液体引入表面波假设与不计表面波动的柔性壁贮液容器在结构振动频率和作用力主矢主矩上的差别.通过对柔性贮箱内液体晃动动力学模型的无量纲化,得到了确定该动力学模型的3个基本参数,数值研究了这3个基本参数对系统固有频率、系统响应力主矢主矩的影响.
The flexibility of container in modeling the liquid slosh in tank and the slosh consideration in modeling the liquid-solid interaction were investigated, including the influence of container's flexibility on liquid slosh and the influence of liquid slosh on the structure vibration. The dynamic model coupling the liquid slosh and the tank's structure oscillation was established. Employing both the eigen-modals of liquid slosh and structure vibration, the coupled boundary value problems of differential equation describing respective liquid slosh and structure vibration are discretized. The dynamic equation of the coupled liquid-solid system is yielded in a matrix form of ordinary differential equation. The corresponding eigen-equation of the liquid-solid coupled system, the computable formulas of resultant forces and moments of both liquid slosh and the coupled system were obtained. The effect of flexibility of tank in liquid slosh problem and the effect of liquid slosh in liquid-solid vibraiton problem were numerically studied through the natural frequencies, the resultant forces and moments. The three decisive parameters were obtained by dimensionless research, and the influence of the parameters was researched by numerical analysis.
The flexibility of container in modeling the liquid slosh in tank and the slosh consideration in modeling the liquid-solid interaction were investigated, including the influence of container's flexibility on liquid slosh and the influence of liquid slosh on the structure vibration. The dynamic model coupling the liquid slosh and the tank's structure oscillation was established. Employing both the eigen-modals of liquid slosh and structure vibration, the coupled boundary value problems of differential equation describing respective liquid slosh and structure vibration are discretized. The dynamic equation of the coupled liquid-solid system is yielded in a matrix form of ordinary differential equation. The corresponding eigen-equation of the liquid-solid coupled system, the computable formulas of resultant forces and moments of both liquid slosh and the coupled system were obtained. The effect of flexibility of tank in liquid slosh problem and the effect of liquid slosh in liquid-solid vibraiton problem were numerically studied through the natural frequencies, the resultant forces and moments. The three decisive parameters were obtained by dimensionless research, and the influence of the parameters was researched by numerical analysis.
引文
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[2] 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.
[3] 魏发远,李世其,黄玉盈,等.浸水圆柱壳振动特性的有限条——边界元分析[J].应用力学学报,2001,18(2):1-6.WEIFa-yuan,LIShi-qi,HUANGYu-ying,etal.StudyonvibrationofcylindricalshellssubmergedinwaterbyFS-BEmethod[J].ChineseJournalofAp-pliedMechanics,2001,18(2):1-6.
[4] 周 叮.计及表面波的圆环形贮液容器的弯曲自由振动[J].应用数学和力学,1994,15(9):789-797.ZHOUDing.Freebendingvibrationofannularcylin-dricalthankpartiallyfilledwithliquidintheconsider-ationofsurfacewave[J].AppliedMathematicsandMechanics,1994,15(9):789-797.
[5] GuptaRK,HutchinsonGL.Effectsofwallflexibili-tyonthedynamicresponseofliquidstoragetanks[J].EngStruct,1991,13(2):253-267.
[6] FischerFD,RammerstorferFG.Arefinedanalysisofsloshingeffectsinseismicallyexcitedtanks[J].In-ternationalJournalofPressureVesselsandPiping,1999,76(6):693-709.
[7] 万 水,朱德懋.圆柱贮液固液耦合模态分析[J].工程力学,2000,17(3):87-92.WANShui,ZHUDe-mao.Solid-liquidcouplingmodalanalysisofcylindricaltank[J].EngineeringMechan-ics,2000,17(3):87-92.
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