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| Theoretical Modeling and Analysis on the Combination Resonance of Rotating Blade |
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| DOI：10.7643/issn.1672-9242.2022.06.011 |
| KeyWord:combination resonance nonlinear vibration rotating cantilever beam L-P method helicopter blade vibration perturbation method |
| Author | Institution |
| LI Zhen-kun |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
| CHENG Qi-you |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
| ZHU Yan |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
| QIAN Feng |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
| LIU Chen |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
| DAI Zhi-xiong |
Science and Technology on Rotorcraft Aeromechanics Laboratory, China Helicopter Research and Development Institute, Jiangxi Jingdezhen , China |
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| Abstract: |
| This paper is to theoretically investigate the combination resonance of a single helicopter rotating blade under two excitation forces. The blade rotates at a fixed angular velocity and is regarded as a rotating slender cantilever beam, which is subjected to two excitation forces with different frequencies. Firstly, the governing equations of the rotating beam are derived with the aid of Hamilton's variation principle, considering large geometric deformation and nonlinear inertia. Secondly, the equations are dimensionless, and the governing equation is discretized by applying the Galerkin scheme. Finally, the L-P method (Lindstedt-Poincare method) in the perturbation approach is applied to solve the dimensionless equation. The conditions of combination resonance are obtained and the steady-state amplitude-frequency response curves, as well as the corresponding time history diagram under the combined resonance are obtained; further obtain the conditions for the simultaneous occurrence of super-harmonic/sub-harmonic resonance and combination resonance, and analyze the parameters of combination resonance to explore the influence of each excitation frequency component, damping and excitation position on the combination resonance. Results reveal that when the two excitation forces satisfy one of the conditions, 2Ω1±Ω2=ω0, Ω2±Ω1=ω0 or 1/2(Ω1±Ω2)=ω0, the combination resonance may occur in the rotating beam; the free vibration part is dominant in combination resonance, and the combination resonance amplitude is further enhanced in the presence of super-harmonic resonance. |
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