项目名称: 基于谱分解的柔度扰动新方法及其在结构损伤识别中的应用
项目编号: No.11202138
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 杨秋伟
作者单位: 绍兴文理学院
项目金额: 24万元
中文摘要: 扰动方法在非线性力学、结构损伤识别、振动控制以及优化设计等领域具有广泛的应用。传统的扰动方法一般是基于级数线性展开的,低阶近似仅对小扰动情况有效。对于大型复杂结构系统,高阶扰动分析的计算量巨大且精度不理想。本项目拟研究一种基于谱分解的柔度扰动新方法。以矩阵谱分解技术为主要手段,研究参数扰动量和柔度改变量之间的内在关系。在此基础上,采用一次谱分解便可获得所有的扰动参数。所提方法在本质上不属于参数小扰动时的线性近似,而是基于参数扰动量和柔度改变量之间的一种直接关系,因此无需进行高阶扰动分析和多次迭代。与传统方法相比,所提方法计算简单且精度更高,且对大扰动情况同样有效。将这种新方法推广应用于结构的损伤识别中,并进行实验验证。本项目拟提出的柔度扰动新方法,不仅是对扰动理论和方法的有益补充,且有望为大型结构损伤识别提供一种新途径,具有重要的理论意义和工程实用价值。
中文关键词: 损伤识别;柔度法;扰动;谱分解;响应参数
英文摘要: The perturbation methods have been widely used in many areas, such as nonlinaer mechanics, structural damage identification, vibration control, optimimal design, and so on. The traditional perturbation techniques are all the linear approximation methods based on the series expansion. Therefore the first-order perturbation analysis can only be used for the small variation of the perturbation parameters. When the changes of structural parameters are relatively large, the high-order perturbation analysis or the iteration scheme is usually performed. But the high-order perturbation or iteration will tremendously increase the computation effort, especially for the large-scale complicated structures. To this end, the aim of this project is to develop a new flexibility perturbation method based on the matrix spectral decomposition. The most significant advantage of the proposed method is that it can yield a reliable structural parameter only by simple computation without any high-order approximations or iterations, regardless of whether the variation of the structural parameter is small or large. The underlying principle of the developed theory is to decompose structural flexibility matrix into a matrix representation of the connectivity between degrees of freedom and a diagonal matrix containing the magnitude informat
英文关键词: damage identification;flexibility method;perturbation;spectral decomposition;response parameters