主动约束层阻尼梁的数值模型

Numerical model of beams with active constrained layer damping

为对主动约束层阻尼结构建立精确完善的数学模型 ,采用有限元建模 ,并考虑到压电材料的机电耦合效应和粘弹性材料的本构关系随温度、频率的变化而变化的特点 ,将有限元方法与粘弹性材料的 GHM模型相结合 ,从而避免因粘弹性材料导致的非线性微分方程 ,能直接求解模态频率、模态阻尼及结构响应。为进一步设计控制器 ,先在物理空间进行动力缩聚 ,将系统降至适当的维数 ,然后在状态空间用鲁棒降阶的方法进一步降阶。这样既能大大降低系统维数 ,又能保证降阶后系统稳定、可控、可观。这对于重量轻、柔度大。

In order to more precisely and perfectly model the active constrained layer damping structures and make good preparations for performing control research, the finite element method is employed. The electromechanical coupling effect of PZT ceramics and the distinguishing feature of the constitute relation of viscoelastic material, which varies with the variety of temperature and frequency, are considered. The finite element method is combined with the GHM model of viscoelastic material so as to transform the nonlinear differential equations, due to the viscoelastic material, to the standard second order time invariant system. This can avoid time consuming iteration and solve the modal frequencies, modal damping ratios and response directly. In order to design a controller, the dynamic condensation is performed in the physical space at first, which results in a reduced order system with suitable size; the robust model reduction method is utilized in succession. The above model reduction process can not only reduce the size of the system greatly but also guarantee the stability, controllability and observability of the final reduced order system. This is especially important for the large space structures with lightweight, large flexibility and close low modal frequencies.