59461 - Topological Optimization of Piezoelectric Transducers for Vibration Reduction of Bladed Disks 

Piezoelectric shunt damping is a promising alternative for bladed disks of fans and compressors where conventional friction dampers have difficulties to deploy with the increasingly use of integral processing technologies and composite materials. It consists in connecting piezoelectric transducers integrated in the host structure to electric circuits. The amount of piezoelectric materials used to achieve the desired damping level should be minimized to control the added mass. In this work, we develop a topological optimization method to determine the best distribution of piezoelectric materials on a given bladed disk. There is no constrain on the shape of piezoelectric materials, and only the overall mass is limited. The targeting modes should also be given before optimization, and could be a single mode or several modes from the same/different modal groups. The method is based on the fact that the modal damping is solely determined by the modal electromechanical coupling factor (MEMCF). Through analytical derivation we show that MEMCF is related to the modal stress field and the geometric 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. This topological method is naturally adopted for finite element model and can be applied after the modal analysis of the bladed disk. The piezoelectric materials were 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 were also presented. The proposed procedure was 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 and disk-blade coupled modes can be achieved. The strength issue of the piezoelectric materials is briefly analysed at the end of the paper.