几何缺陷对拱结构动力稳定性的影响
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摘要
分析了外激励下几何缺陷对拱结构动力稳定性的影响。推导了拱结构边界确定而结构本身节点坐标偏差随机且指数相关时的条件相关矩阵,分解得到几何缺陷的分布方式和大小。从非线性运动方程出发,分别得出了周期荷载作用下非线性刚度矩阵可线性化,非周期荷载作用下同时考虑几何、材料非线性的Lyapunov指数计算方法。最后以一圆弧拱为例分别对周期荷载、阶跃荷载、脉冲荷载及地震荷载作用下几何缺陷的影响进行了数值分析。结果表明周期激励作用下拱结构存在动力失稳频域;在不同分布方式几何缺陷中动力稳定性对与屈曲模态相似的缺陷最为敏感。
This paper is concerned with the effects of geometrical imperfections on the dynamic stability of arch structure under external load.The conditional covariance matrix of stochastic arch structure,whose node coordinate deviations are exponentially correlative,is determined by deterministic boundary conditions,and through the decomposition of the matrix the distribution shapes and amplitude of geometrical imperfections are obtained.From the nonlinear motion equation,the top Lyapunov exponents for periodic load,in which the nonlinear stiffness matrix can be linearized,and for non-periodic load,where both geometrical and material nonlinearities are taken into account,are determined respectively.And a circular arch is taken as an example to investigate the effects of geometrical imperfections under periodic load,step load,impulsive load and earthquake load.The results show that the buckling frequency regions exist under periodic excitation and the dynamic stability is most sensitive to the geometrical imperfection that is similar to the static buckling mode.
This paper is concerned with the effects of geometrical imperfections on the dynamic stability of arch structure under external load.The conditional covariance matrix of stochastic arch structure,whose node coordinate deviations are exponentially correlative,is determined by deterministic boundary conditions,and through the decomposition of the matrix the distribution shapes and amplitude of geometrical imperfections are obtained.From the nonlinear motion equation,the top Lyapunov exponents for periodic load,in which the nonlinear stiffness matrix can be linearized,and for non-periodic load,where both geometrical and material nonlinearities are taken into account,are determined respectively.And a circular arch is taken as an example to investigate the effects of geometrical imperfections under periodic load,step load,impulsive load and earthquake load.The results show that the buckling frequency regions exist under periodic excitation and the dynamic stability is most sensitive to the geometrical imperfection that is similar to the static buckling mode.
引文
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[9]Yeo MH,Lee WK.Evidences of global bifurcations of an imperfect circular plate[J].Journal of Sound and Vibration,2006,293(1-2):138-155.
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[11]Vanmarcke E.Random fields:analysis and synthesis[M].MITPress,Cambridge,1983:25-61.
[12]Nordgren R P,Conte J P.On one-dimensional random fields with fixed end values[J].Probabilistic Engineering Mechanics,1999(14):301-310.
[13]Kratzig W B,Nawrotzki P.Computational concepts in structural stability[J].Archives of Computational Methods in Engineering,1996,3(1):81-119.
[14]王勖成,邵敏.有限单元法基本原理和数值分析[M].北京:清华大学出版社,1996:541-564.
[2]李忠学.初始几何缺陷对网壳结构静、动力稳定性承载力的影响[J].土木工程学报,2002,35(1):11-15.
[3]叶继红,沈祖炎.初始缺陷对网壳结构动力稳定性能的影响[J].土木工程学报,1997,30(1):37-42.
[4]郭海山,钱宏亮,沈世钊.地震作用下单层球面网壳结构的动力稳定性[J].地震工程与工程振动,2003,23(1):31-37.
[5]Most T,Bucher C,Schorling Y.Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading[J].Journal of Sound and Vibration,2004,276(1/2):381-400.
[6]Schorling Y,Bucher C.Dynamic stability analysis for structures with geometrical imperfections[M]//Structural Safety and Reliability,Balkema,Rotterdam:Naruhito Shiraishi,Masanobu Shinozuka,Y K Wen(Eds.),1998:771-777.
[7]Schorling Y,Bucher C.Stochastic stability of structures with random imperfections[M]//Stochastic Structural Dynamics,Balkema,Rotterdam:B F Spencer Jr.,E A Johnson(Eds.),1999:343-348.
[8]Bielewicz E,G幃rski J.Shells with random geometric imperfections simulation-based approach[J].International Journal of Non-Linear Me-chanics,2002(37):777-784.
[9]Yeo MH,Lee WK.Evidences of global bifurcations of an imperfect circular plate[J].Journal of Sound and Vibration,2006,293(1-2):138-155.
[10]Elishako I,Zingales M.Contrasting probabilistic and anti-optimization approaches in an applied mechanics problem[J].International Journal ofSolids and Structures,2003,40(16):4281-4297.
[11]Vanmarcke E.Random fields:analysis and synthesis[M].MITPress,Cambridge,1983:25-61.
[12]Nordgren R P,Conte J P.On one-dimensional random fields with fixed end values[J].Probabilistic Engineering Mechanics,1999(14):301-310.
[13]Kratzig W B,Nawrotzki P.Computational concepts in structural stability[J].Archives of Computational Methods in Engineering,1996,3(1):81-119.
[14]王勖成,邵敏.有限单元法基本原理和数值分析[M].北京:清华大学出版社,1996:541-564.
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