标准特征值问题扰动分析的精确方法

发布时间：2018-12-24 07:00

【摘要】：在扰动量存在的情况下,准确计算特征值的扰动量是确保结构安全性的重要问题.针对标准特征值问题扰动分析提出了一种精确方法,能够高效地计算特征值扰动量的准确值,克服了矩阵摄动级数展开法忽略高阶项导致的计算精度不足的缺点.提出的方法推导得到了标准特征值问题扰动分析求解方程.求解方程推导过程中没有经过近似处理,将求解标称系统标准特征值问题方程得到的特征值标称值代入,就能求得特征值扰动量的准确值,从而能够有效满足高精度和高效率要求.3个数值算例分别对所提出的精确方法进行了验证,与矩阵摄动级数展开法的计算结果相比,能够准确高效地计算特征值的扰动量,具有精确和高效的双重优势.
[Abstract]:It is an important problem to calculate the disturbance of eigenvalue accurately in the presence of disturbance quantity to ensure the security of the structure. In this paper, an accurate method for perturbation analysis of standard eigenvalue problems is proposed, which can efficiently calculate the exact values of eigenvalue perturbations, and overcomes the shortcoming that the matrix perturbation series expansion method neglects the high order terms. The perturbation analysis equation of the standard eigenvalue problem is derived by the proposed method. In the derivation of the equation, the exact value of the perturbation of the eigenvalue can be obtained by substituting the nominal value of the eigenvalue obtained by solving the equation of the standard eigenvalue problem of the nominal system without approximate treatment. The proposed method is verified by three numerical examples. Compared with the results of matrix perturbation series expansion method, the perturbation of eigenvalues can be calculated accurately and efficiently. It has the dual advantage of precision and efficiency.
【作者单位】：北京航空航天大学航空科学与工程学院固体力学研究所;
【基金】：国家自然科学基金(11372025,11432002) 国防基础科研计划基金(JCKY2013601B001,JCKY2016204B101,JCKY2016601B001) 科技部民用飞机专项(MJ-F-2012-04) 国家重点研发计划(2016YFB0200704) 高等学校学科创新引智计划(B07009)资助
【分类号】：O241.6

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