Nonlinear aeroelastic behavior of a two-dimensional heated panel by irregular shock reflection considering viscoelastic damping

Abstract

This paper investigates the aeroelastic stability and nonlinear aeroelastic behavior of a two-dimensional heated panel in irregular shock reflection and extends prior work to include the effects of viscoelasticity. The aeroelastic model is formulated using the von Kármán large deflection plate theory and the Kelvin–Voigt damping model, accompanied by the quasi-steady thermal stress theory. The unsteady aerodynamic pressure is evaluated through the piston theory and the compressibility-corrected potential theory. The Galerkin approach is used to discretize the governing equation. The Lyapunov indirect method is applied to conduct theoretical analysis, obtaining the aeroelastic stability boundary. Also, the nonlinear aeroelastic response is numerically simulated via the fourth-order Runge–Kutta method. The proper orthogonal decomposition is applied to the panel deflection to manifest the influence of various system parameters. It is demonstrated that the shock wave aggravates the aerodynamic heating, lowering the critical buckling temperature. The viscoelastic damping restricts the impact of shock impingement location and shock strength on the stability boundary and also transforms the chaotic motions into periodic LCOs.