Abstract
Heated curved panels flutter in supersonic air flow will affect fatigue
life and flight performance of aircrafts, thus the research on heated
curved panels flutter was an important problem in flight design. A
nonlinear aero-elastic partial differential equation for two-dimensional
heated curved panels in supersonic flow was established based on the
von-Karman nonlinear strain-displacement relation and aerodynamic force
model of supersonic flow, which was described by improved piston theory.
The aero-elastic partial differential equation was derived to a
four-dimensional ordinary differential equation system by using second
order Galerkin discretization method. The algebraic criterion of the
Hopf bifurcation was utilized in the equation system to derive the Hopf
bifurcation point of the system (also the flutter critical
value).Therefore, analytical expressions of flutter critical dynamic
pressure and vibration frequency were theoretically derived. Then, a
numerical experiment was established, and the agreement of numerical
result and theoretical value was validated. The result showed that
flutter dynamic pressure decreased and then increased with initial
curvature rising. For small curvature panel, flutter dynamic pressure
also first decreased and then increased with temperature rising, while
for large curvature panel flutter dynamic pressure always increased with
temperature rising. The established equation system and analytical
expression of Hopf bifurcation point can provide some guidance for
heated curved panel in supersonic air flow.