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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。
The main work of this dissertation focuses on the simple and accurate prediction of the modal frequency of the tall steel chimney. Firstly, according to the characteristics of the tall steel chimney, its dynamic differential equation is established and is unobstructed by coordinate transformation and dimensionless normalization The free-vibration partial differential equations are discretized. Subsequently, the Adomian decomposition method (Adomian decomposition method, ADM) is introduced and the modal frequencies are solved by introducing the boundary conditions and continuous conditions. Secondly, according to the data of the towering steel chimney collected, the distribution rules of the existing partially chimney steel chimneys are statistically calculated, and random sampling is conducted to obtain the fitted samples. Finally, three simplified calculation expressions of modal frequencies of tall steel chimney were obtained by the method of stepwise regression and piecewise linear regression. The fitting accuracy of various expressions was analyzed. The results show that the expression obtained by the method of piecewise linear regression can calculate the modal frequency of the tall steel chimney relatively efficiently. The research work in this paper can provide certain reference for the design of tall steel chimney and the revision of the corresponding codes.