用于叶片减振的压电材料分布拓扑优化

Topological optimization of piezoelectric materials on the blades for vibration reduction of bladed disks

提出一种可用于实际叶盘结构的压电分支阻尼器拓扑优化方法,可以给出总质量受约束的压电材料在叶片上的最佳分布,达到尽可能大的模态阻尼比。通过理论推导说明:压电阻尼器所产生的模态阻尼比仅取决于模态机电耦合系数,且该系数只与压电材料的几何形状以及模态应力场有关。进一步结合压电本构关系,基于应力分量的线性加权给出了有限的压电材料在叶片上铺设位置"优先级"的判断指标。给出了基于叶盘结构有限元模型的压电材料拓扑优化方法,通过替换单元类型和材料参数的方式对压电材料进行布置,并给出了多模态族优化、极化方向设置、电极铺设等问题的解决方案。在一个接近真实的叶盘模型上应用了此优化方法。结果表明,仅使用质量占叶片质量10%的压电材料,就可以为多个模态提供约12%的阻尼比。

A topological optimization procedure of piezoelectric shunting damping for arbitrary full-scale bladed disks was proposed.Based on the fact that the modal electromechanical coupling factor(MEMCF)is the only parameter that affecting the level of modal damping ratios produced by piezoelectric shunting circuit.Further,it showed that MEMCF was related to modal stress field and the geometry of the piezoelectric materials only.Combining with piezoelectric constitutive relation,a linear weighting of stress components was proposed as the criterion to determine the priority of locations for piezoelectric materials.Accordingly,the topological optimization procedure was presented based on the finite element model of bladed disk,where the piezoelectric materials were introduced by modifying the type and material parameters of elements.Solutions for optimization with respect to multiple modal families,polarized direction setting,and electrode connection were also presented.The proposed procedure was applied to an empirical bladed disk.Results show that 12% damping ratio can be achieved for multiple modes using piezoelectric materials with mass of only 10%of the blade.