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 zero equilibrium state and find a critical value of the velocity 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.