Effect of Turbomachinery Blade Root Flexibility on Electromechanical Coupling for Piezoelectric-Based Vibration Reduction

摘要

The last two decades have seen a wealth of interest in utilizing piezoelectric materials for turbomachinery applications. These approaches rely on the piezoelectric materials efficiently converting energy between the mechanical and electrical domains and requires locating the piezoelectric materials in regions of high modal strain on the vibrating blade to target the vibration modes of interest. When considering a turbomachinery blade, the boundary conditions at the blade root can affect the dynamics of the blade such that a piezoelectric material that is optimized for the stand-alone blade may no longer be optimal with the blade attached to the disk. This paper investigates the effects that the root flexibility has on the electromechanical coupling for blade-mounted piezoelectric materials. Analysis of a lumped-parameter blisk model shows that the electromechanical coupling largely depends on the spatial harmonic of the associated blisk mode shape. For the modes where the the disk stores the majority of the strain energy, there is minimal coupling; whereas for the modes where the blades store the majority of the strain energy, the coupling converges to the quantity associated with the the stand-alone blade with the disk fixed. A subsequent analysis utilizes a representative blade model that incorporates discrete springs at the blade root to simulate the disk flexibility. The stiffness of the blade root can significantly alter the blade mode shapes and corresponding distribution of strain energy and, consequently, the electromechanical coupling for the various modes.