低矮小开口剪力墙自由振动问题的半解析解
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摘要
针对低矮小开口剪切型剪力墙,研究基于直接模态摄动法原理的结构动力特性的半解析分析方法。首先把低矮小开口剪力墙视为变截面的剪切型悬臂结构,依据连续系统动力分析原理建立剪切型剪力墙自由振动分析的变系数微分方程;然后利用等截面剪切型悬臂结构模态函数的解析解和直接模态摄动法原理,考虑剪力墙中小开口对系统特征值和主模态所带来的影响,并进行修正;最后应用Ritz变换,将低矮小开口剪力墙的自振特性分析问题转化为一组非线性代数方程的求解问题,进而求得该类剪力墙自振特性的近似半解析解。算例结果表明,该方法对以剪切变形影响为主的低矮小开口剪力墙动力分析简便有效。
Based on the principal of direct modal perturbation method,a simplified semi-analytical technique for the modal characteristics of the short shear wall with small openings was developed.At first,the short shear wall with small openings was considered as a shear cantilever system with variable cross sections.The differential equation of motion with variable coefficient of the system was established according to the dynamic analysis theory of the distributed-parameter systems.Then,the effects of the small openings in the shear wall on the modal characteristics of the shear cantilever system with variable cross sections were discussed and modified utilizing the modal characteristics of the shear cantilever system having uniform properties and the direct modal perturbation.Finally,a set of nonlinear algebraic equations was obtained by applying Ritz transformation to solve the modal characteristics of the short shear wall with small openings.The results of numerical examples show that the proposed method is simplification and has good precision.
Based on the principal of direct modal perturbation method,a simplified semi-analytical technique for the modal characteristics of the short shear wall with small openings was developed.At first,the short shear wall with small openings was considered as a shear cantilever system with variable cross sections.The differential equation of motion with variable coefficient of the system was established according to the dynamic analysis theory of the distributed-parameter systems.Then,the effects of the small openings in the shear wall on the modal characteristics of the shear cantilever system with variable cross sections were discussed and modified utilizing the modal characteristics of the shear cantilever system having uniform properties and the direct modal perturbation.Finally,a set of nonlinear algebraic equations was obtained by applying Ritz transformation to solve the modal characteristics of the short shear wall with small openings.The results of numerical examples show that the proposed method is simplification and has good precision.
引文
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[13]CHENG F Y.Matrix Analysis of Structural Dynam-ics:Applications and Earthquake Engineering[M].New York:Marcel Dekker Inc.,2000.
[2]刘伯权,潘元.框架-抗震墙结构抗震墙抗弯刚度的优化研究[J].建筑科学与工程学报,2005,22(1):55-57.LIU Bo-quan,PAN Yuan.Study on Optimum BendingRigdity of Seismic Wall in Frame-Shear Wall Struc-ture[J].Journal of Architecture and Civil Engineer-ing,2005,22(1):55-57.
[3]沈蒲生,刘杨.水平地震作用下框支剪力墙结构的变形研究[J].建筑科学与工程学报,2005,22(1):58-63.SHEN Pu-sheng,LIU Yang.Distortion Research ofShear Wall Structure Supported on Frame UnderEarthquake Actions[J].Journal of Architecture andCivil Engineering,2005,22(1):58-63.
[4]易伟建,张颖.混凝土框架结构抗震设计的弯矩增大系数[J].建筑科学与工程学报,2006,23(2):46-51.YI Wei-jian,ZHANG Ying.Moment MagnificationFactor in Anti-seismic Design of Concrete FrameStructure[J].Journal of Architecture and Civil Engi-neering,2006,23(2):46-51.
[5]张永健,黄平明.考虑剪力滞效应的简支箱梁自振特性[J].建筑科学与工程学报,2005,22(2):40-42.ZHANG Yong-jian,HUANG Ping-ming.Free Vibra-tion Characteristics of Simply Supported Box Girderwith Effect of Shear Lag[J].Journal of Architectureand Civil Engineering,2005,22(2):40-42.
[6]史庆轩,杨文星,门进杰.单自由度体系非线性地震能量反应的计算[J].建筑科学与工程学报,2005,22(2):25-29.SHI Qing-xuan,YANG Wen-xing,MEN Jin-jie.Cal-culation of Seismic Energy Response for NonlinearSingle Degree of Freedom System[J].Journal of Ar-chitecture and Civil Engineering,2005,22(2):25-29.
[7]沈聚敏,周锡元,高小旺,等.抗震工程学[M].北京:中国建筑工业出版社,2000:416-418.SHEN Ju-min,ZHOU Xi-yuan,GAO Xiao-wang,et al.Aseismic Engineering[M].Beijing:China Archi-tecture&Building Press,2000:416-418.
[8]黄东升,程文瀼.短肢剪力墙结构动力特性分析的半解析法[J].振动工程学报,2005,18(3):309-313.HUANG Dong-sheng,CHENG Wen-rang.DynamicAnalysis for Short-Pier Walls by Semi-analytic Ap-proach[J].Journal of Vibration Engineering,2005,18(3):309-313.
[9]夸克工作室.有限元分析基础篇ANSYS与Matlab[M].北京:清华大学出版社,2002.Quarx Studio.Fundamental Finite Element Analysiswith ANSYS and Matlab[M].Beijing:Tsinghua Uni-versity Press,2002.
[10]楼梦麟,吴京宁.复杂梁动力问题的近似分析方法[J].上海力学,1997,18(3):234-240.LOU Meng-lin,WU Jing-ning.An Approach to SolveDynamic Problems of Complicated Beams[J].Shang-hai Journal of Mechanics,1997,18(3):234-240.
[11]楼梦麟,白建方.FRP加固梁模态分析的摄动解法[J].建筑科学与工程学报,2005,22(2):21-24.LOU Meng-lin,BAI Jian-fang.Perturbation Solutionfor Modal Characteristics of Beam Strengthened byFRP[J].Journal of Architecture and Civil Engineer-ing,2005,22(2):21-24.
[12]LOU Meng-lin,DUAN Qiu-hua,CHEN Gen-da.Mo-dal Perturbation Method for the Dynamic Characteris-tics of Timoshenko Beams[J].Shock and Vibration,2005,20(12):425-434.
[13]CHENG F Y.Matrix Analysis of Structural Dynam-ics:Applications and Earthquake Engineering[M].New York:Marcel Dekker Inc.,2000.
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