Keywords: panel flutter, aeroelasticity, nonlinear analysis, finite element analysis, supersonic speeds, composite plates.

Panel flutter is the self-excited oscillation of the external skin of a flight vehicle when exposed to airflow along its surface. The use of linear structural theory indicates that there is a critical dynamic pressure above which the panel motion becomes unstable. For large deflections, the nonlinear effects, the induced mid-plane forces restrain the panel motion to bounded limit cycle oscillations (LCO). At supersonic speeds, the skin panel temperatures could reach several hundred degrees due to aerodynamic heating. Large aero-thermal deflections of the skin panel may occur. With the presence of supersonic flow and temperatures, four types of panel behavior are observed and they are flat and stable, aero-thermally buckled but dynamically stable, LCO, and chaos.

The various classical methods start with the governing partial differential equations in conjunction with the Galerkin's method (PDE/Galerkin) [1], and the finite element methods start with the system equations of motion in physical structural node degrees of freedom [2] for nonlinear supersonic panel flutter analysis. Both PDE/Galerkin and finite element methods employ a reduced base approach to reduce the PDE or the finite element system equations to a set of coupled nonlinear ordinary differential equations using vacuo natural modes (NMs). It is commonly accepted that a minimum of six NMs is needed for converged LCO of isotropic rectangular plates at zero yaw angle [1]. For isotropic or orthotropic rectangular plates under an arbitrary nonzero yawed supersonic flow, 36 or 6 6 NMs are needed; for laminated anisotropic rectangular plates even at zero yaw angle, 36 or fewer NMs are needed [3].

A major advance to further reduce the number of coupled nonlinear modal equations is the use of aeroelastic modes (AEMs) [4]. With the presence of aerodynamic effects in the NMs, which are the AEMs, only two to six AEMs are needed for converged LCO of isotropic or anisotropic composite rectangular plates at zero or an arbitrary yawed flow angle [4]. This paper is the first time to extend the use of AEMs to nonlinear panel flutter analyses considering both nonzero yawed supersonic flow and elevated temperatures. It is demonstrated that only six AEMs are needed, instead of 36 (6 6) or fewer NMs, for nonlinear supersonic panel flutter at an arbitrary yawed flow angle and elevated temperatures. It is also shown that all four types of panel motion can be determined.

1

E.H. Dowell, "Panel Flutter: A Review of the Aeroelastic Stability of Plate and Shells," AIAA Journal, 8, 386-399, 1970. doi:10.2514/3.5680

2

C. Mei, K. Abdel-Motagaly, R. Chen, "Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds," Applied Mechanics Reviews, 52, 321-332, 1999. doi:10.1115/1.3098919

3

K. Abdel-Motagaly, R. Chen, C. Mei, "Nonlinear Flutter of Composite Panels Under Yawed Supersonic Flow Using Finite Elements," AIAA Journal, 37, 1025-1032, 1999. doi:10.2514/2.818

4

X. Guo and C. Mei, "Using Aeroelastic Modes for Nonlinear Panel Flutter at Arbitrary Supersonic Yawed Angle," AIAA Journal, 41, 272-279, 2003. doi:10.2514/2.1940

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