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.