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Super-harmonic resonances of a rotating pre-deformed blade subjected to gas pressure

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Abstract

The present work investigates the super-harmonic resonances combined with 2:1 internal resonance of a rotating blade subjected to strong gas pressure. The dynamic model includes the effect of the initial curved axis of the blade induced by the thermal gradient. The dimensionless gas excitation amplitude is assumed to be the same magnitude of the dimensionless vibration displacement. The vibration of the blade in the plane of rotation and the plane perpendicular to it are described by a set of coupled ordinary differential equations with quadratic and cubic nonlinearities. The steady-state response of the rotating blade is calculated via the method of multiple scales. The stabilities of the steady-state responses are determined via Lyapunov theory. Parametric studies are performed to clarify the influences of system parameters on dynamic response and unstable regions. The various typical phenomena including jump, hysteresis and saturation are observed in the dynamic model. The stable and unstable regions of the solution are analyzed in the plane of external detuning parameter and excitation amplitude. The evaluation of the blade dynamic response is revealed in the unstable region. The theoretical results obtained via the method of multiple scales coincide with the numerical solutions.

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Acknowledgements

This project is supported by National Natural Science Foundation of China (Grant Nos. 11702033 and 11572182), the Fundamental Research Funds for the Central Universities (Grant No. 300102128107) and Innovation Program of Shanghai Municipal Education Commission (No. 2017-01-07-00-09-E00019).

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200444, China

    Bo Zhang, Hu Ding & Li-Qun Chen

  2. School of Science, Chang’an University, Xi’an, 710064, Shaanxi, China

    Bo Zhang

  3. School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

    Li-Qun Chen

  4. Shanghai Key Laboratory of Energy Engineering Mechanics, Shanghai, 200444, China

    Li-Qun Chen

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  1. Bo Zhang
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Correspondence to Li-Qun Chen.

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Zhang, B., Ding, H. & Chen, LQ. Super-harmonic resonances of a rotating pre-deformed blade subjected to gas pressure. Nonlinear Dyn 98, 2531–2549 (2019). https://doi.org/10.1007/s11071-019-05367-x

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