基于反馈控制技术的结构动力学模型修正

发布时间：2018-04-03 03:27

本文选题：反馈控制　切入点：模型修正　出处：《湖北师范大学》2017年硕士论文

【摘要】：有限元模型修正技术是当前结构动力学领域的重要研究方向之一.模型修正的主要内容就是对一个实际结构进行试验测试,然后利用测试结果对结构的分析模型进行修正,使得修正后的模型给出的分析结果与相应的试验结果具有良好的相关性,即修正后的模型能较准确地描述实际结构.本文主要讨论具体内容如下:第一章介绍了本文所需的符号,引理和论文的安排.第二章首先讨论了基于反馈控制技术的无阻尼结构模型修正问题,运用矩阵的QR分解和迭代算法得到了满足特征方程的加速度和位移反馈增益矩阵,同时还得到了在Frobenius范数下,满足要求的最优修正质量和刚度矩阵.该方法不仅可以保证修正后的矩阵是对称的,同时还可以保证修正是不溢出的.其次,考虑了基于输出反馈控制技术的无阻尼结构模型修正问题,通过运用矩阵的QR分解、奇异值分解和迭代算法得到了满足特征方程的加速度和位移输出反馈增益矩阵,同时还得到了满足要求的最优修正质量和刚度矩阵.该方法不仅可以保证修正后的矩阵是对称的,同时还可以保证修正是不溢出的.最后,考虑了一类特殊情况下的基于反馈控制技术的无阻尼结构模型修正问题.数值例子显示我们的方法是可靠有效的.第三章讨论了基于反馈控制技术的阻尼结构模型修正问题.运用矩阵的QR分解和迭代算法得到了满足特征方程的速度和位移反馈控制增益矩阵,同时还得到了在Frobenius范数下,满足要求的最优修正阻尼和刚度矩阵.该方法不仅把测得的特征数据嵌入到了新的模型中,同时保证修正后的系统仍然是对称的.
[Abstract]:Finite element model modification is one of the most important research directions in the field of structural dynamics.The main content of the model modification is to test a real structure, and then modify the analysis model of the structure by using the test results.The result of the modified model has a good correlation with the corresponding experimental results, that is, the modified model can describe the actual structure more accurately.The main contents of this paper are as follows: the first chapter introduces the symbol, Lemma and the arrangement of the paper.In the second chapter, the problem of undamped structure model modification based on feedback control technique is discussed. The acceleration and displacement feedback gain matrices satisfying the characteristic equations are obtained by using the QR decomposition and iterative algorithm of the matrix. At the same time, under the Frobenius norm, the acceleration and displacement feedback gain matrices are obtained.The optimal modified mass and stiffness matrix to meet the requirements.This method can not only guarantee that the modified matrix is symmetric, but also guarantee that the modified matrix is not overflow.Secondly, the problem of undamped structure model modification based on output feedback control technique is considered. By using QR decomposition, singular value decomposition and iterative algorithm, the acceleration and displacement output feedback gain matrices satisfying the characteristic equations are obtained.At the same time, the optimal modified mass and stiffness matrix are obtained.This method can not only guarantee that the modified matrix is symmetric, but also guarantee that the modified matrix is not overflow.Finally, the problem of undamped structural model modification based on feedback control is considered.Numerical examples show that our method is reliable and effective.In chapter 3, the problem of model modification of damping structure based on feedback control is discussed.The velocity and displacement feedback control gain matrices satisfying the characteristic equations are obtained by using the QR decomposition and iterative algorithm of the matrix. The optimal modified damping and stiffness matrices satisfying the requirements are also obtained under the Frobenius norm.This method not only embeds the measured characteristic data into the new model, but also ensures that the modified system is still symmetric.
【学位授予单位】：湖北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O342

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