analysing panel flutter in supersonic flow by hopf bifurcation

this paper is devoted to study of a partial differential equation governing panel motion in supersonic flow. this pde can be transformed to an ode by means of a galerkin method. here by using a criterion which is closely related to the routh-hurwitz criterion, we investigate the mentioned transformed ode from hopf bifurcation point of view. in fact we obtain a region for existence of simple hopf bifurcation for it. with the aid of computer language matlab and hopf bifurcation tool, flutter and limit cycle oscillations of panel are verified. moreover, hopf bifurcation theory is used to analyse the flutter speed of the system.