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利用传统的一阶选频内平衡降阶方法进行降阶时,不但破坏了原二阶系统动力学结构,而且降阶过程中的选频Gramian矩阵的求解计算量大、数值稳定性差。利用解耦模态坐标的二阶柔性空间结构(FSS)方程的特殊性,给出了可控和可观Gramian矩阵的选频闭合解析解。为了将FSS动力学模型在指定频段进行降阶并保留原系统的二阶动力学结构,提出了几种不同的二阶选频降阶方法。数值仿真结果表明,所提出的降阶方法可以有效地在指定频段进行降阶,降阶精度可以达到或超过传统的一阶选频内平衡降阶方法。
When using the traditional first-order FSB method to reduce the order, not only the original second-order system dynamics structure is destroyed, but also the calculation of the frequency-selective Gramian matrix in the reduced order is large and the numerical stability is poor. Using the particularity of the second-order flexible space structure (FSS) equation with decoupled modal coordinates, the frequency-selective closed analytic solutions of controllable and observable Gramian matrices are given. In order to reduce the FSS dynamic model in the specified frequency band and preserve the second-order dynamic structure of the original system, several different second-order frequency-selective reduction methods are proposed. Numerical simulation results show that the proposed reduced order method can effectively reduce the order of the specified frequency band, and the accuracy of the reduced order can meet or exceed the traditional first-order frequency-balanced solution reduction method.