Local bifurcations of nonlinear viscoelastic panel in supersonic flow

The stability and bifurcation behaviors of a two-dimensional nonlinear viscoelastic panel in supersonic flow are investigated with analytical and numerical methods. One type of critical points for the bifurcation response equations is considered, which is characterized by a pair of purely imaginary eigenvalues and a pair of complex conjugate eigenvalues having negative real part. With the aid of computer language Maple and the normal form theory, Hopf bifurcation solution of the model is investigated. Finally, numerical simulations are shown, which agree with the theoretical analytical results.

► The stability and bifurcation behaviors of the two-dimension nonlinear supersonic panel are proposed.
► Norm form is obtained through a systematic and efficient computation method.
► Hopf bifurcation may occur in the two-dimension nonlinear supersonic panel.
► Stability conditions of the steady state solutions are determined.
► Numerical solutions are obtained, which agree with the analytical results.