Abstract: This study concerns the application of piezoelectric shunt damping in the vibration reduction of the bladed disks in aero-engines. A topology optimization method for the distribution of the piezoelectric materials on the disk of a blisk modal is proposed. The method enables the maximum damping with a restricted amount of piezoelectric materials. Moreover, bonding the piezoelectric materials on the disk prevents the interference to the fluid field and therefore it preserves the fluid efficiency. First, the theoretical basis of the topology optimization is introduced. The modal electromechanical coupling coefficient (MEMCF) is the critical parameter relating the modal strain field, the modal frequency and the best damping ratio. Its calculation formula is derived. Second, the topology optimization is proposed based on the modal strain field. Note that this method is applicable to arbitrary structures once the finite element models are given. Eventually, the proposed method is applied in a compressor bladed disk of aeroengine, where both the single-mode and multi-mode situations are considered, to study its effects on the damping in different modes(disk dominant, blade dominant and disk-blade coupled modes). When the mass of piezoelectric materials is only 5% of the disk, the optimized piezoelectric damper can provide up to 13% modal damping ratio for the disk dominant and disk-blade coupled modes. On the other hand, modal damping ratio achieved for the blade dominant modes focuses on 2%~4%.

Key words: Piezoelectric shunt damping;Bladed disk;Vibration reduction;Modal electromechanical coupling coefficient (MEMCF);Topology optimization

摘要： 针对压电分支阻尼技术在航空发动机叶盘结构振动抑制问题中的应用，提出了一种拓扑优化方法，可给出限定用量的压电材料在轮盘上的最佳位置，以提升压电分支阻尼的上限。在轮盘上布置压电材料还可防止对叶片通道内流场的影响，避免降低流体效率。首先，论述了该拓扑优化方法的原理，推导了模态机电耦合系数这一核心参数的计算公式及其与最佳阻尼比、模态应变场的关系。其次，建立了基于模态应变场的压电材料分布拓扑优化方法，可用于任意有限元模型。最后，将该优化方法应用于一个航空发动机压气机叶盘结构模型，分别针对单一和多阶模态进行了压电材料在轮盘上分布的拓扑优化，研究这种铺设方式对各典型模态（轮盘主导、叶片主导、耦合振动）的振动抑制效果。结果表明,在仅采用占轮盘质量5%的压电材料的情况下，优化后的压电阻尼器最多可以为轮盘振动主导模态及叶片-轮盘耦合振动模态提供约13%的模态阻尼比，为叶片主导模态提供的模态阻尼比集中在2%~4%。

关键词: 压电分支阻尼;叶盘结构;振动抑制;机电耦合系数;拓扑优化