钢制储液罐的Lyapunov特征指数及弹性动力失稳
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摘要
为全面评估钢制储液罐在地震激励下的动力稳定性能,由压力-位移格式的流固耦合模型建立等效动力扰动方程,采用时变几何刚度矩阵参数化结构域抗力,修正广义扰动变量并实时调整向量模长,进而步进求解动态Lyapunov特征指数,分别在简谐地面加速度与地震激励下对某10万m3油罐进行动力稳定分析.结果表明:上述Lyapunov方法确定的动力不稳定域与Floquet方法基本一致;Lyapunov方法与B-R准则法计算的临界地震动峰值存在10%左右的最大相对误差;抗风圈有助于抑制动力不稳定域并提高临界地震动峰值.上述Lyapunov方法适用于二阶动力系统,可考虑地震持时影响且不限制地震波特性,大幅降低了动力稳定分析的计算成本并能满足工程应用精度.
To comprehensively evaluate the dynamic stability of liquid storage tanks under earthquake excitations,the equivalent dynamic perturbation equations were established based on coupled fluid-solid model with displacement-pressure form,the resistance force in structure domain was parameterized by time-varying geometric stiffening matrix,the generalized perturbation variables were then modified and the vector length was adjusted in real-time,and the dynamic Lyapunov characteristic exponents were then solved with time-stepping techniques,by which the dynamic stability analysis of a 100 000m3 oil storage tank was respectively executed under harmonic and earthquake ground motions.The results show that the dynamic instability regions obtained by the above Lyapunov method were essentially consistent with the estimates of Floquet method,and the maximum relative error of critical peak ground acceleration calculated by Lyapunov method and B-R criteria method is appoximately 10 %,and the wind girders are helpful to inhibit dynamic instability regions and improve the critical peak ground acceleration.The proposed Lyapunov method is suitable for second-order dynamic systems,can consider the effect of earthquake duration,anddoes not restrict the characteristics of seismic waves.Moreover it also dramatically reduces the computing cost of dynamic stability analysis and meets the precision requirement for engineering application.
To comprehensively evaluate the dynamic stability of liquid storage tanks under earthquake excitations,the equivalent dynamic perturbation equations were established based on coupled fluid-solid model with displacement-pressure form,the resistance force in structure domain was parameterized by time-varying geometric stiffening matrix,the generalized perturbation variables were then modified and the vector length was adjusted in real-time,and the dynamic Lyapunov characteristic exponents were then solved with time-stepping techniques,by which the dynamic stability analysis of a 100 000m3 oil storage tank was respectively executed under harmonic and earthquake ground motions.The results show that the dynamic instability regions obtained by the above Lyapunov method were essentially consistent with the estimates of Floquet method,and the maximum relative error of critical peak ground acceleration calculated by Lyapunov method and B-R criteria method is appoximately 10 %,and the wind girders are helpful to inhibit dynamic instability regions and improve the critical peak ground acceleration.The proposed Lyapunov method is suitable for second-order dynamic systems,can consider the effect of earthquake duration,anddoes not restrict the characteristics of seismic waves.Moreover it also dramatically reduces the computing cost of dynamic stability analysis and meets the precision requirement for engineering application.
引文
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[6]Takayanagi M.Parametric resonance of liquid storage axisymmetric shell under horizontal excitation[J].Journal of Pressure Vessel Technology,1990,113:511-516.
[7]杨宏康,高博青.基于Floquet理论的储液罐动力稳定性分析[J].浙江大学学报:工学版,2013,47(2):379-384.YANG Hong-kang,GAO Bo-qing.Dynamic stability analysis of liquid storage tanks based on Floquet theory[J].Journal of Zhejiang University:Engineering Science,2013,47(2):379-384.
[8]Virella J C,Godoy L A,Suarez L E.Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation[J].Journal of Constructional Steel Research,2006,62(6):521-531.
[9]Buratti N,Tavano M.Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method[J].Earthquake Engineering&Structural Dynamics,2014,43(1):1-21.
[10]Skokos C,Gerlach E.Numerical integration of variational equations[J].Physical Review E,2010,82(3):036704.
[11]Skokos C.The Lyapunov charactaristic exponents and their computation[J].Lecture Notes in Physics,2010,790:63-135.
[12]Moslemi M,Kianoush M R.Parametric study on dynamic behavior of cylindrical ground-supported tanks[J].Engineering Structures,2012,42:214-230.
[13]Crisfield M,Remmers J,Verhoosel C.Nonlinear finite element analysis of solids and structures.2nd ed[M].Chichester,UK:John Wiley&Sons,2012:169-215.
[14]Chopra A K.Dynamics of structures:theory and applications to earthquake engineering.4th ed[M].New Jersey:Prentice-Hall,2012:447-466.
[15]郭洪亮.某港口10万m3大型储油罐静动力有限元分析[D].大连:大连理工大学,2006.
[16]GB50011—2010.建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.
[17]GB50341—2003.立式圆筒形钢制焊接油罐设计规范[S].北京:中国计划出版社,2003.
[2]Chen Z,Sun B,Yu C,et al.Comparison of the strength design and prevention method of elephant foot buckling among countries'standards of oil tanks[C]∥Proceedings of the ASME 2009pressure vessels and piping division conference.Prague,Czech Republic:ASME,2009:461-466.
[3]Chiba M,Tani J,Hashimoto H,et al.Dynamic stability of liquid-filled cylindrical shells under horizontal excitation,part I:experiment[J].Journal of Sound and Vibration,1986,104(2):301-319.
[4]Fukuyama M,Nakagawa M,Ishihama K,et al.Dynamic buckling experiments of fluid-structure-coupled co-axial thin cylinder[J].Nuclear Engineering and Design,1999,188(1):13-26.
[5]Maekawa A,Shimizu Y,Suzuki M,et al.Vibration test of a 1/10reduced scale model of cylindrical water storage tank[J].Journal of Pressure Vessel Technology,2010,132(5):125-137.
[6]Takayanagi M.Parametric resonance of liquid storage axisymmetric shell under horizontal excitation[J].Journal of Pressure Vessel Technology,1990,113:511-516.
[7]杨宏康,高博青.基于Floquet理论的储液罐动力稳定性分析[J].浙江大学学报:工学版,2013,47(2):379-384.YANG Hong-kang,GAO Bo-qing.Dynamic stability analysis of liquid storage tanks based on Floquet theory[J].Journal of Zhejiang University:Engineering Science,2013,47(2):379-384.
[8]Virella J C,Godoy L A,Suarez L E.Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation[J].Journal of Constructional Steel Research,2006,62(6):521-531.
[9]Buratti N,Tavano M.Dynamic buckling and seismic fragility of anchored steel tanks by the added mass method[J].Earthquake Engineering&Structural Dynamics,2014,43(1):1-21.
[10]Skokos C,Gerlach E.Numerical integration of variational equations[J].Physical Review E,2010,82(3):036704.
[11]Skokos C.The Lyapunov charactaristic exponents and their computation[J].Lecture Notes in Physics,2010,790:63-135.
[12]Moslemi M,Kianoush M R.Parametric study on dynamic behavior of cylindrical ground-supported tanks[J].Engineering Structures,2012,42:214-230.
[13]Crisfield M,Remmers J,Verhoosel C.Nonlinear finite element analysis of solids and structures.2nd ed[M].Chichester,UK:John Wiley&Sons,2012:169-215.
[14]Chopra A K.Dynamics of structures:theory and applications to earthquake engineering.4th ed[M].New Jersey:Prentice-Hall,2012:447-466.
[15]郭洪亮.某港口10万m3大型储油罐静动力有限元分析[D].大连:大连理工大学,2006.
[16]GB50011—2010.建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.
[17]GB50341—2003.立式圆筒形钢制焊接油罐设计规范[S].北京:中国计划出版社,2003.
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