A method for the resonant response evaluation of blades system with underplatform dampers

The friction damper has been widely used to reduce the resonant vibration of blades. The harmonic balance method is a well-known method for the linearization of the nonlinear friction force. Meanwhile Mindlin gives analytical expression to describe the nonlinear friction force during stick contact condition, therefore the nonlinear force is represented by two linear coefficients, i.e., equivalent stiffness and equivalent damping. In this work, the stiffness matrix and mass matrix are normalized to a lumped mass and corresponding stiffness according to the definition of stiffness and modal mode. For blades system with underplatform dampers, the dynamic equation for multi lumped mass system is derived and also the iteration method is listed. At last, the experiment verification is conducted using 2 plate blades with underplatform damper. The comparison shows a good agreement in both resonant response and resonant frequency for low normal load cases, and still capture the tendency for high normal load cases.