Hopf Bifurcation of Heated Panels Flutter in Supersonic Flow

被引:8
作者
Cao, Li-Na [1 ,2 ]
Yao, Guofeng [1 ]
机构
[1] Jilin Univ, Sch Mech & Aerosp Engn, Changchun 130025, Jilin, Peoples R China
[2] Changchun Univ Technol, Sch Mech Sci & Engn, Changchun 130012, Jilin, Peoples R China
关键词
panels; hopf-bifurcation; thermal flutter; Hurwitz determinant; COMPOSITE LAMINATED PANELS; TEMPERATURE;
D O I
10.3390/math7090787
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
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页数:10
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