Linear Vibration of the Rotary Plate Under Combined Excitations in Subsonic Airflow

Abstract

Due to strong nonlinear, unsteady characteristics and the fluid–structure interaction effect, vibration analysis of blades under the excitation of the airflow is still one of the technical difficulties. In this paper, the accurate subsonic aerodynamic force is obtained through numerical simulation, and the aerodynamic coupling model of the rotary blade is established. The distribution of the aerodynamic force of the compressor blade under the unsteady airflow is focused on. The blade is modeled as presetting a presetting pre-twisted rotary cantilever plate. Dynamic frequencies of the plate, calculated by Chebyshev–Ritz method, are compared with frequencies calculated using the finite element method (FEM). Effects of different parameters on natural frequencies of the rotary plate are discussed. Based on von-Karman nonlinear geometric relation and the first-order shear deformation theory, nonlinear dynamic equations of the pre-twisted rotary plate under the combination of the centrifugal force and the aerodynamic are derived by utilizing Hamilton’s principle. Second-order ordinary differential equations are derived by applying the Galerkin method. Analytical solution of the dynamic deformation of the plate is presented and is compared with that produced by FEM. Results indicate the accuracy of the explicit presentation of the aerodynamic of the low-pressure compressor blade. Effects of the rotary speed, the thickness, the pre-twisted angle and the presetting angle on vibration characteristics of the warping blade are studied. Mode shape shift and frequency loci veering are discussed.