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Intermittency in pitch-plunge aeroelastic systems explained through stochastic bifurcations

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Abstract

Aeroelastic systems with hardening nonlinearity exhibit supercritical Hopf bifurcation when the flow velocity exceeds a critical velocity leading to self-sustaining large amplitude limit cycle oscillations known as flutter. This study investigates the effects of irregular fluctuations in the flow on the dynamical stability characteristics of a two-degree-of-freedom pitch-plunge aeroelastic system with hardening nonlinearity. Dynamical or D-bifurcations are investigated through the computation of the largest Lyapunov exponent, while phenomenological or P-bifurcation analysis is carried out by examining the structure of the joint probability density function of the response quantities and their instantaneous time derivatives. The qualitative nature of P-bifurcation analysis makes it difficult to pinpoint the regimes of different response dynamics. In the light of this difficulty, a quantitative analysis using the Shannon entropy measure has been undertaken to quantify the P-bifurcation regime. This regime is shown to be coincident with the intermittency regime observed in the response time histories prior to flutter oscillations in fluctuating flows.

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Authors and Affiliations

  1. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai, 600036, India

    J. Venkatramani & Sayan Gupta

  2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai, 600036, India

    Sunetra Sarkar

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  1. J. Venkatramani
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  2. Sunetra Sarkar
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  3. Sayan Gupta
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Correspondence to Sayan Gupta.

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Venkatramani, J., Sarkar, S. & Gupta, S. Intermittency in pitch-plunge aeroelastic systems explained through stochastic bifurcations. Nonlinear Dyn 92, 1225–1241 (2018). https://doi.org/10.1007/s11071-018-4121-5

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  • DOI: https://doi.org/10.1007/s11071-018-4121-5

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