Design of dry friction and piezoelectric hybrid ring dampers for integrally bladed disks based on complex nonlinear modes

This paper investigates a new passive damper coupling the energy dissipative mechanisms of dry friction and piezoelectric shunting circuit for Integrally Bladed Disks (blisks). The idea is to distribute piezoelectric material to the dry friction ring so that the elastic deformation of the dry friction ring is utilized to generate additional damping. Mounting piezoelectric material on the additional structure instead of the host structure is a more practical alternative to install piezoelectric damping devices to realistic mechanical systems. This improves the reliability and maintainability of both dampers and host structures. Based on the concept of Complex Nonlinear Modes (CNMs), the dry friction damping effect of the proposed damper is measured through the modal damping ratio for target modes. Modal Electromechanical Coupling Factor (MEMCF) is extended to nonlinear electromechanical coupling systems in order to quantify the additional piezoelectric damping ratio. The damping effect of the hybrid damper is also evaluated by the maximal response amplitude in the frequency domain by the forced response analysis. On one hand, it validates the results from the nonlinear modal analysis, on the other hand, it serves as a reference to choose the optimum design parameters of the hybrid damper. Steady-state response of the cyclic symmetric structure under engine-order excitation is calculated by the Multi-Harmonic Balance Method (MHBM). A phenomenological lumped parameter model representing a blisk with a hybrid ring damper is firstly studied to demonstrate the methodology. Then a blisk finite element model is used as a demonstrator to quantitatively verify the effectiveness of the idea. It is shown that for those modes that can be damped by the dry friction damper, the addition of piezoelectric material further enhances the damping effect.