Aeroelastic effect on aerothermoacoustic response of metallic panels in supersonic flow

A finite element formulation is presented for the analysis of the aeroelastic effect on the aerothermoacoustic response of metallic panels in supersonic flow. The first-order shear deformation theory (FSDT) and the von Karman nonlinear strain-displacement relationships are employed to consider the geometric nonlinearity induced by large deflections. The piston theory and the Gaussian white noise are used to simulate the mean flow aerodynamics and the turbulence from the boundary layer. The thermal loading is assumed to be steady and uniformly distributed, and the material properties are assumed to be temperature independent. The governing equations of motion are firstly formulated in structural node degrees of freedom by using the principle of virtual work, and then transformed and reduced to a set of coupled nonlinear Duffing oscillators in modal coordinates. The dynamic response of a panel is obtained by the Runge-Kutta integration method. The results indicate that the increasing aeroelastic effect can lead the panel vibration from a random motion to a highly ordered motion in the fashion of diffused limit cycle oscillations (LCOs), and remarkably alter the stochastic bifurcation and the spectrum of the aerothermoacoustic response. On the other hand there exists a counterbalance mechanism between the external random loading and the aeroelastic effect, which mainly functions through the nonlinear frequency-amplitude response. It is surmised that the aeroelastic effect must be considered in sonic fatigue analysis for panel structures in supersonic flow.