线性粘弹结构有限元模型的鲁棒降阶方法

摘要

为了对粘弹性材料复合结构进行静动力分析及主被动控制，采用微振子模型描述线性粘弹材料的本构关系，先用有限元方法对结构进行离散，然后引入耗散自由度，将非线性的有限元方程转化为普通的二阶系统，最后从系统的可控性、可观性出发提出了一种模型的鲁棒降阶方法。算例表明微振子模型与有限元相结合，能很方便地求出固有频率、阻尼等模态参数及响应。鲁棒降阶算法稳定，能为下一步进行主动控制做好准备。%In order to perform the static or dynamic analysis and passive or active control for the viscoelastic composite structures,the Mini-Oscillator model is adopted to describe the constitutive relation of viscoelastic material.The finite element method(FEM)is employed to discrete the structure at first,and then the dissipated coordinates are introduced so as to transform the nonlinear FEM equations into ordinary second order system.Finally a robust model reduction method is proposed in view of the controllability and the observability of the system.The numerical example shows that it is very convenient to calculate the natural frequency,modal damping or other modal parameters and the response after the Mini-Oscillator model is combined with FEM.The model reduction method proposed is quite robust.The order reduced system is good enough for active control.