Topological Optimization of Piezoelectric Transducers for Vibration Reduction of Bladed Disks

Abstract

In this work, we develop a numerical method to determine the best distribution of piezoelectric materials on a given bladed disk, so as to minimize the added mass of shunted piezoelectric dampers. There is no constrain on the shape of piezoelectric materials, and only the overall mass is limited. The method can be applied to a single mode or several modes from the same or different modal groups. The method is based on the fact that the modal damping is solely determined by the modal electromechanical coupling factor (MEMCF) which is related to the modal stress field and the geometric of the piezoelectric materials only. A linear weighting of stress components is proposed as the criterion to determine the priority of locations for piezoelectric materials. The piezoelectric materials are introduced to the FE model by modifying the type and materials parameters of elements if they are embedded to the bladed disks; or by creating an additional layers of elements if they are bonded to the bladed disks. Details for considering multiple modes, handling polarization direction and electrode connection are also presented. The proposed procedure is applied to an empirical bladed disk with NASA-ROTOR37 profile. Results show that 12% damping ratio can be achieved for multiple modes simultaneously, if we locate piezoelectric materials on the blade with 10% added mass. When locate the piezoelectric materials on the disk and the added mass is only 5%, up to 13% modal damping ratio for the disk dominant modes can be achieved.