Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

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