一类二阶振动矩阵方程的求解

On the Solution of a Class of Second-order Vibration Matrix Equations

研究了一类二阶振动矩阵方程的求解问题,该方程在振动控制领域得到广泛应用。针对具有约当对角标准型的特征值情形,提出了一种求解该二阶振动矩阵方程的参数化方法。该参数化方法给出了该矩阵方程中两个未知矩阵的完全参数化表达式,其含有自由参量为二阶振动矩阵方程的解提供了全部自由度。最后,利用所提出的二阶振动矩阵方程的参数化方法对数值算例进行了求解,结果表明该参数化方法的简单和有效性。

Solution of a class of second-order vibration matrix equations is investigated, which are widely used in vibration control fields. In the case of the eigenvalues with the Jordan diagonal canonical form, a parametric method is proposed. The proposed method offers the complete parametric expressions of two unknown matrices in the second-order vibration matrix equation, and the parameters presents all the degrees of freedom for the solution of second-order vibration matrix equation. Finally, using the proposed parametric method is solved a numerical example and the results show the simplicity and effectiveness of the proposed parametric method.