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

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

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,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4期26-35,共10页China Civil Engineering Journal

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

摘　　要：主要围绕简单而精确地对高耸钢烟囱模态频率进行预测展开研究工作:首先,根据高耸钢烟囱的特点,建立了其动力微分方程,并通过坐标变换和无量纲归一化的方法对其无阻尼自由振动的偏微分方程进行了离散;随后,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频率进行了求解。其次,通过搜集的高耸钢烟囱资料,统计了现有部分高耸钢烟囱参数分布规律,并以此进行了随机抽样,得到拟合样本。最后,采用逐步回归和分段线性回归的方法,得到了高耸钢烟囱模态频率三种简化计算表达式,并对各类表达式的拟合精度进行了分析。研究表明:采用分段线性回归的方法得到的表达式能够相对高效地计算高耸钢烟囱的模态频率。本文的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。This study focuses on predicting the modal frequency of high-rise steel chimneys in a simple and accurate way. Firstly, the dynamic differential equation of high-rise steel chimney is established according to its characteristics, and then it is decomposed through coordinate transformation and dimensionless procedures. By introducing boundary conditions and continuity conditions, modal frequencies of high-rise steel chimney can be solved using Adomian Decomposition Method （ADM）. Secondly, the statistical distributions of steel chimney＇ s key parameters are investigated based on the collected information, and then the sample data are obtained by employing random sampling method. Lastly, three simplified expressions of steel chimney＇ s modal frequency are fitted by stepwise regression method and piecewise linear regression method, and the accuracy of these expressions is also analyzed. The results show that the function obtained by piecewise linear regression method can predict the modal frequency of steel chimneys more efficiently. 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 频率 ADOMIAN分解法 多元回归分析 

分 类 号：TU311.3[建筑科学—结构工程] TU391