Nonlinear Panel Flutter. Bolotin’s Problem in the Presence of Viscous Friction

In this paper, we consider a nonlinear boundary-value problem proposed as the simplest model for describing oscillations in a gas flow. We analyze the stability of the trivial (zero) equilibrium state and find a critical value of the speed of the incoming gas flow. Exact solutions of the problem are found in the form of time-periodic functions and their stability is examined. All the results are obtained analytically based on the qualitative theory of infinite-dimensional dynamical systems.