用不完全模态试验数据修正粘性阻尼矩阵

假定质量矩阵、刚度矩阵、复振型是精确的或已修正的，研究用不完全复模态试验数据修正粘性阻尼矩阵。依据特征方程、粘性阻尼矩阵的对称性和半正定性，利用代数特征值反问题的理论和方法，给出了问题解的存在性和唯一性，提出了修正粘性阻尼矩阵的一个新方法。用这个方法修正的粘性阻尼矩阵不仅满足特征方程，而且是唯一的最优对称半正定矩阵。最后用两个例子说明本文方法的有效性。

Updating of the viscous damping matrix from incomplete modal experimental data

The problem of updating the viscous damping matrix from incomplete com plex modal experimental data is considered . It is assumed that the complex mode shapes , the mass and the stiffness matrices are accurate or have been updated b efore . Based on the characteristic equation , the symmetry and positive semidef initeness of the viscous damping matrix , the existence and uniqueness of soluti on to the problem is studied by means of the theory and method of the algebraic inverse eigenvalue problems. A new method of updating the viscous damping matrix is presented . The viscous damping matrix corrected by the method not only sati sfies the characteristic equation but also is the unique optimized symmetric pos itive semidefinite matrix .The proposed method is demonstrated by means of two e xamples.