A novel dynamic model on nonlinear vibrations of functionally graded graphene platelet reinforced rotating pretwisted composite blade considering subsonic airflow excitation and blade-casing rubbing

Abstract

A novel dynamic model of the functionally graded graphene platelet (FGGP) reinforced rotating pretwisted composite blade under the aerodynamic force and blade-casing rubbing is established for the first time. The blade is simplified to a FGGP reinforced rotating pretwisted composite cantilever plate. The dynamic model of the axial excitation produced by considering the aerodynamic force in the tip clearance includes two trigonometric functions with different frequencies. The subsonic airflow is considered as a transverse excitation which is derived by utilizing the vortex lattice method (VLM). The dynamic model expresses the changes of the non-uniform axial and contact forces through the tip clearance and rotating pretwisted plate-casing rubbing when the shaft is eccentric. Based on Rayleigh-Ritz method, the linear frequencies and mode shapes are obtained for the FGGP reinforced rotating pretwisted plate. The influences of the graphene distribution pattern, rotating pretwisted plate-casing rubbing, axial excitation in the tip clearance and geometric parameter on the frequencies are investigated. Using the obtained mode shapes, von-Karman type nonlinear geometric assumptions and Lagrange equation, the differential governing equations of motion are derived for the FGGP reinforced rotating pretwisted plate. The nonlinear vibrations under the 1:1 internal resonance at two critical rotating speeds is studied by using Runge-Kutta method. The amplitude-frequency and force-frequency response curves under the low and high critical rotating speeds are investigated by using numerical calculations. The obtained results demonstrate the influence of the rotating speed, frequency ratios and incoming flow speeds on the nonlinear vibrations of the FGGP reinforced rotating pretwisted plate. The dynamic model of the rubbing-impact for the rotating blade provides a theoretical basis for the blade-casing rubbing analysis. At the same time, this study is also used as a theoretical guidance to reduce the damage of the blade-casing rubbing and blade design.