基于Adomian分解和回归分析的高耸钢烟囱动力特性研究(Ⅱ):模态振型  

Study on dynamic characteristics of high-rise steel chimneys based on Adomian decomposition method and regression analysis(Ⅱ):Modal shape

作　　者：陈鑫[1,2] 李爱群[2] 程文瀼[2] 王泳 

机构地区：[1]苏州科技学院,江苏苏州215011 [2]东南大学混凝土及预应力混凝土结构教育部重点实验室,江苏南京210096 [3]苏州云白华鼎烟囱制造有限公司,江苏苏州215003

出　　处：《土木工程学报》2013年第6期69-75,共7页China Civil Engineering Journal

基　　金：国家杰出青年基金(50725858);东南大学优秀博士论文基金(YBJJ1006)

摘　　要：模态振型是精确分析结构风振响应的关键之一,主要围绕高耸钢烟囱模态振型展开研究工作:首先,采用Adomian分解法(Adomian decomposition method,ADM),并引入边界条件和连续条件对模态振型进行求解;随后,以论文(Ⅰ)统计得到的高耸钢烟囱参数分布规律,进行随机抽样,得到拟合样本;最后,借助回归分析的方法,分别用欧洲规范(Eurocode)表达式、多项式、指数函数求和、正弦函数求和、傅里叶级数等表达式对高耸钢烟囱的无量纲模态振型进行拟合,得到高耸钢烟囱前四阶模态振型表达式,并对各类表达式的拟合精度、复杂程度和适用情况进行讨论。研究表明:多项式和傅里叶级数形式的振型表达式更适用于进一步的风振统一理论研究。本研究工作能够为高耸钢烟囱的设计和相应规范的修订提供一定的参考。Modal shape is one of the key factors for analyzing wind induced responses, and hence in this work the modal shape of high-rise steel chimneys is studied. Firstly, after the boundary conditions and continuity conditions being introduced, the modal shape is solved via Adomian Decomposition Method （ADM）. Secondly, the sample data of modal shape are obtained using random sampling method based on the statistical distributions of the parameters of high steel chimneys, as investigated in previous studies of the authors. Lastly, the expressions of dimensionless modal shape, which contain the Eurocode function, polynomial, summation of exponential function, summation of Sine function and Fourier series, are fitted by introducing regression analysis method. Then the expressions of first four modal shapes are presented, and the fitting precision, complexity and applicability of all expressions are also discussed. The results show that the expression in the form of Polynomial or Fourier series is more suitable for the further investigation of unified wind vibration theory. This work may offer some reference for the design of high-rise steel chimneys and the revision of relevant codes.

关 键 词：高耸钢烟囱 动力特性 振型 ADOMIAN分解法 多元回归分析 

分 类 号：TU311.3[建筑科学—结构工程] TU391