一般黏性阻尼振动系统的实空间解耦与自由界面模态综合法

发布时间：2018-10-15 16:38

【摘要】：一般黏性阻尼振动系统通常可变换到状态空间,利用解得的复模态可以将系统方程解耦,但解耦后的方程是复系数方程,必须在复数域内进行求解。根据所需要保留的复特征解对的特征,通过复特征向量矩阵的线性变换构造了一种新的模态变换关系,利用模态变换矩阵将一般黏性阻尼振动系统的状态空间运动方程变换为解耦的实系数二阶常微分方程。随后,构造了一种与实变换矩阵关于系统矩阵加权正交的向量集,利用这种加权正交的向量集推导系统剩余柔度矩阵时可以避免对系统矩阵进行直接求逆,解决了含刚体模态时的系统剩余柔度矩阵的求解问题。然后,将实空间解耦和加权正交向量集与自由界面模态综合法相结合,推导出了与常规振动微分方程具有相同形式的实系数系统综合方程。最后,通过数值算例验证了方法的有效性。
[Abstract]:The general viscous damping vibration system can be transformed into state space, and the system equations can be decoupled by using the complex modes, but the decoupled equations are complex coefficient equations, which must be solved in the complex domain. According to the characteristics of the pair of complex characteristic solutions which need to be preserved, a new mode transformation relationship is constructed by the linear transformation of the complex eigenvector matrix. The state space equation of motion of a general viscous damping vibration system is transformed into a decoupled second order ordinary differential equation with real coefficients by means of the modal transformation matrix. Then, we construct a vector set weighted orthogonal to the real transformation matrix about the system matrix. When we use the weighted orthogonal vector set to derive the residual flexibility matrix of the system, we can avoid directly inverse the system matrix. The problem of solving the residual flexibility matrix of the system with rigid body mode is solved. Then, the real space decoupling and weighted orthogonal vector sets are combined with the free interface modal synthesis method, and the synthesis equations of the real coefficient system with the same form as the ordinary vibration differential equations are derived. Finally, the effectiveness of the method is verified by numerical examples.
【作者单位】：机械结构力学及控制国家重点实验室;南京航空航天大学振动工程研究所;
【基金】：国家自然科学基金资助项目(11472132) 中央高校基本科研业务费资助项目(NS2014002) 机械结构力学及控制国家重点实验室(南京航空航天大学)自主研究课题资助项目(0113Y01) 江苏高校优势学科建设工程资助项目
【分类号】：O321

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