Abstract
High speed rotating blades are crucial components of modern large aircraft engines. The rotating blades under working condition frequently suffer from the aerodynamic, elastic and inertia loads, which may lead to large amplitude nonlinear oscillations. This paper investigates nonlinear dynamic responses of the blade with varying rotating speed in supersonic airflow. The blade is simplified as a pre-twist and presetting cantilever composite plate. Warping effect of the rectangular cross-section of the plate is considered. Based on the first-order shear deformation theory and von-Karman nonlinear geometric relationship, nonlinear partial differential dynamic equations of motion for the plate are derived by using Hamilton’s principle. Galerkin approach is applied to discretize the partial differential governing equations of motion to ordinary differential equations. Asymptotic perturbation method is exploited to derive four-degree-of-freedom averaged equation for the case of 1 : 3 internal resonance-1/2 sub-harmonic resonance. Based on the averaged equation, numerical simulation is used to analyze the influence of the perturbation rotating speed on nonlinear dynamic responses of the blade. Bifurcation diagram, phase portraits, waveforms and power spectrum prove that periodic motion and chaotic motion exist in nonlinear vibration of the rotating cantilever composite plate.
Highlights
High-speed rotating blades are essential components of modern large aircraft engines
Various types of excitation lead to large amplitude nonlinear parametric vibrations of the blades, which can result in the resonance phenomena and undesirable disasters, especially when the rotating blades operate with high speed and huge centrifugal force
The vibration failure of the aircraft engine is more than 60% of the total failure, while the vibration failure of the blade accounts for more than 70% of the total vibration failure
Summary
High-speed rotating blades are essential components of modern large aircraft engines. Sinha and Turner [10] derived governing partial differential equations of motion for a rotating pretwist plate to investigate the static and dynamic frequencies of the blade. Zhang and Li [19] adopted the Lagrangian method to acquire dynamic equations of motion for the pretwist and predeformed rotating cantilever plate subjected to the harmonic aerodynamic force. According to large deformation geometric relationship, the piston theory and the quasi-static thermal stress theory, Yuan and Qiu [33] established the aerodynamic model of a composite stiffened panel and used Hamilton’s principle to derive the equations of motion for the system. In order to analyze the internal resonance, we choose the perturbation rotating speed as the controlling parameter to investigate nonlinear behaviors of the pretwist and presetting rotating cantilever plate. Since we can control the responses of the system from the chaotic motions to the periodic motions by changing the perturbation rotating speed, we can control the large amplitude nonlinear vibrations of the blade
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