加肋圆柱曲板房顶的非线性垂直地震响应

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英文篇名：NONLINEAR DYNAMLIC RESPONSE OF REINFORCED CYLINDRICAL CURVED PLATE ROOFS SUBJECTED TO VERTICAL SEISMIC FORCE 中文刊名：地震研究 英文刊名：JOURNAL OF SEISMOLOGICAL RESEARCH 作者：范磊 ; 范家参 英文作者：Fan Lei 1) Fan Jianshen 2) (Engineering Division ; Shenzhen Haishen Co. Ltd. ; Shen Zhen ; 518003) 1) (Department to Civil Engineering ; Yunnan Polytechnic University ; Kunming ; 650051) 2) 中文关键词：加肋圆柱曲板 ; 非线性Rayleigh阻尼 ; 垂直地震响应 ; 动力稳定 英文关键词：Reinforced cylindrical curved plate ; nonlinear Rayleigh damping ; vertical seismic response ; dynamic stability 出版日期：1999-07-03 机构：深圳海神置业有限公司工程部!518003,云南工业大学建工系!650051 年：1999 期：03 出版单位：地震研究

摘要

因纵横向加肋密度不同， 故把题述房顶当做各向异性弹性体［１］ ， 则问题的控制方程组为两个四阶偏微分方程（ 有一个是非线性） ， 代满足边界条件的振型函数入内并用富氏级数的正交性并结合逐次逼近法， 化控制方程组为一个非线性ｖａｎ ｄｅｒ Ｐｏｌ 方程， 得出问题的解析解， 并且讨论了解的跳跃即动力稳定丧失出现的情况。
Considering the densely reinforced cylindrical curved plate roof as anisotropical curved plate and adopting the nonlinear Rayleigh damping, the governing equations are constituted by two PDEs, one of which is nonlinear. Selecting the unknown functions to fulfill all the boundary conditions with coefficients as functions of time variable only, the governing equations are deduced to be one van der Pol equation which is nonhomogeneous, and its analytical solution is known. The jumping phenomenon is discussed.

引文

[1] 中国科学院力学研究所固体力学研究室板壳组, 加筋圆柱板与圆柱壳, 科学出版社, 北京,(1988) ,2 —10 .
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    [4] 胡聿贤,地震工程学,地震出版社,北京,(1998) ,162 ,640 - 642
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    [8] Fan Jiashen and Li Jibin ,dynemic stability ofliquid storage cylindricaltanks sabjected to horizontalseismic force excitation ,ibid , Vol .18 , No .7 , (1994) ,373 - 383 .