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Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

Author

Listed:
  • Li-Na Cao

    (School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China
    School of Mechanical Science & Engineering, Changchun University of Technology, Changchun 130012, China)

  • Guofeng Yao

    (School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China)

Abstract

A differential equation of panel vibration in supersonic flow is established on the basis of the thin-plate large deflection theory under the assumption of a quasi-steady temperature field. The equation is dimensionless, and the derivation of its second-order Galerkin discretization yields a four-dimensional system. The algebraic criterion of the Hopf bifurcation is applied to study the motion stability of heated panels in supersonic flow. We provide a supplementary explanation for the proof process of a theorem, and analytical expressions of flutter dynamic pressure and panel vibration frequencies are derived. The conclusion is that the algebraic criterion of Hopf bifurcation can be applied in high-dimensional problems with many parameters. Moreover, the computational intensity of the method established in this work is less than that of conventional eigenvalue computation methods using parameter variation.

Suggested Citation

  • Li-Na Cao & Guofeng Yao, 2019. "Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow," Mathematics, MDPI, vol. 7(9), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:787-:d:260932
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    References listed on IDEAS

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    1. L. Zhang & L. S. Ling & Z. Qu & W. Tong & S. Tan & Y. H. Zhang, 2010. "Study of lattice dynamics in the CuIr 2 S 4 system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(1), pages 83-86, September.
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    Cited by:

    1. Yuan-Cheng Zhu & Guo-Feng Yao & Min Wang & Kui-Yang Gao & Qi Hou, 2022. "A New Pre-Stretching Method to Increase Critical Flutter Dynamic Pressure of Heated Panel in Supersonic Airflow," Mathematics, MDPI, vol. 10(23), pages 1-16, November.

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