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

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.