二次特征矩阵表示的特征值有界性分析

采用二次特征矩阵近似表示精确有限元和精确动态子结构分析中得出的超越或非线性动态刚度阵，并证明了在满足一定条件的前提下，二次特征阵给出的特征值是精确刚度阵特征值的上界或下界。

BOUNDING PROPERTIES OF THE EIGENVALUES PROVIDED BY A QUADRATIC EIGEN-MATRIX FORMULATION

Approximate representation of a transcendental or a non-linear dynamic stiffnessmatrix K(p) by a quadratic eigen-matrix is studied theoretically in this paper, The quadraticmatrix is formed by expressing the elements of K(p)as parabolic functions based on choosingthree fixed values of the eigenparameter. General bounds on the exact eigenvalues of thetranscendental eigenvalue problem provided by the quadratic matrix are shown to exist ifthe three fixed values chosen are below the lowest pole of the transcendental stiffness matixand the three coefficient matrices of the quadratic formulation are positive definite,It isproved that the approximate quadratic eigen-matrix gives either upper or lower bound oncorresponding exact eigenvalues obtained from the transcendental stiffness matrix.