【作者】 桂冰；

【导师】 戴华；

【作者基本信息】 南京航空航天大学 ， 一般力学与力学基础， 2005， 博士

【摘要】 结构动力模型修正是当前结构动力学领域一个重要的研究方向。本文主要研究结构动力模型修正中的数学理论与方法,研究了一类特殊结构模型修正问题,并为线性结构有限元动力模型修正提供了有效的数值方法。全文工作主要由以下5个部分组成。1.中心对称结构的动力模型修正问题。先讨论一类矩阵方程存在中心对称解的充分必要条件,给出解的一般表达式,并在解集合中给出了与给定矩阵的最佳逼近解。然后,将结果应用于中心对称结构的动力模型修正问题中,对给定的矩阵束,求出满足特征方程且具有中心对称特性的最佳矩阵束逼近。2.考虑到实际问题中具有中心对称特点的矩阵束不一定满足特征方程,进而研究一类矩阵方程最小二乘中心对称解及其最佳逼近,从而给出模型修正中的最小二乘中心对称矩阵束。3.研究了阻尼中心对称结构动力模型修正问题,对给定的三重矩阵(质量矩阵、刚度矩阵和阻尼矩阵),求满足谱约束条件且具有中心对称特性的“最接近”的三重矩阵,并给出数值算例。4.对线性结构的有限元动力模型修正问题,通过灵敏度分析,确定要修正的参数,由正交性条件和特征方程得到相应的修正量方程。为了改善方程组的病态程度,构造了预处理矩阵,利用预处理共轭梯度,给出一个有效的模型修正算法。该算法可用于测量自由度数目等于或小于分析模型自由度的动力模型修正。对于阻尼结构动力模型修正,可由复模态的正交条件和特征方程建立修正方程,应用所给的数值算法求修正量。由模型修正的工程实例,表明修正后模态参数较好地接近实测模态参数。5.给出了线性结构有限元模型修正误差矩阵范数最小的一类新准则。由于测试数据的误差,不能保证正交性条件和特征方程准确成立,为此考虑其方程组最小二乘解作为约束条件,此时将模型修正问题转化为二次约束最小二乘问题。利用奇异值分解,给出一个精度较高的新方法。当测量自由度小更多还原

【Abstract】 The structural dynamics models updating have become increasingly important in the structural dynamics field. This dissertation was to study the mathematical theories and methods for structural dynamical model updating. It gave the solutions and the numerical methods of a special structure model updating. It is composed of five parts:1. The centrosymmetric structural dynamical models updating were studied in the paper. The necessary and sufficient condition for centrosymmetric solution of matrix equation was presented and general solutions were obtained. The optimal approximation solution to a given matrix was provided in the solution set. The results were then applied to solve the centrosymmetric structural dynamical model updating problems. The optimal solution was entreated for the given pencil of matrices.2. Considering pencil of matrices with centrosymmetric could not satisfy characteristic equations in practice, it was necessary to study the centrosymmetric solution of the matrix equation least square problems, and to give pencil of matrices with centrosymmetric of the least squares problems in model updating. 3. The Centrosymmetric structural dynamical systems with damping were studied. The nearest triple matrix of the Centrosymmetric with satisfying characteristic equations was found to a given triple matrix(mass、stiffness and damping matrices). Finally, numerical examples were given.4. A new method for updating linear structural dynamic model was proposed in the paper. The modified parameters were determined by sensitivity analysis. Based upon the orthogonal condition and the characteristic equation of the modal analysis theory, updating equations about the mass and stiffness matrices of the structure were constructed at first. A pretreatment matrix was given and then a stable iterative method was introduced to solve the modified structural parameters. This method was also utilized to update the model of damped dynamic structures.更多还原