Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

Li-Na Cao and Guofeng Yao
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Li-Na Cao: School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China
Guofeng Yao: School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China

Mathematics, 2019, vol. 7, issue 9, 1-10

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.

Keywords: panels; hopf-bifurcation; thermal flutter; Hurwitz determinant (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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