Saturation phenomena and nonlinear resonances of rotating pretwisted laminated composite blade under subsonic air flow excitation

Abstract

The purpose of the present investigation is to reveal the saturation phenomena and the primary resonance of a rotating pretwisted laminated composite blade subjected to a subsonic airflow excitation in the case of 1:2 internal resonance. The flexible compressor blade is treated as a rotating laminated composite cantilever rectangular plate clamped on the rigid disk with the pretwisted and the preset angles. The subsonic air flow is regarded as the transverse excitation around the finite length of the plate. The subsonic air force is derived by using Vortex Lattice method. The third-order shear deformation plate theory, von Karman geometry nonlinearity and Hamilton principle are utilized to derive the nonlinear partial differential governing equations of motion for the rotating plate subjected to the subsonic aerodynamic force. Chebyshev-Ritz method is used to obtain the natural frequencies of the composite cantilever plate with varying rotating speed. Using Galerkin method, the partial differential governing equations of motion is discretized into a two-degree-of-freedom nonlinear system. The nonlinear torsional-bending coupled vibrations with 1:2 internal response are investigated by the method of multiple scales. The saturation and the jumping phenomena between the torsional vibration mode and the bending vibration mode are investigated for the rotating cantilever plate. Numerical simulations demonstrate that the rotating plate exhibits the complicated nonlinear dynamic behaviors under the effect of the excitation detuning parameter, damping parameter and stiffness coupling coefficients. The energy transfer phenomenon is observed for the composite cantilever plate under the subsonic air flow force.