Stability of viscoelastic cylindrical shells in supersonic flow

Based on the Karman-Donnell theory of thin shells, the first order piston theory in aerodynamics and the Boltzmann superposition principles in viscoelasticity, a mathematical model of viscoelastic cylindrical shells in supersonic flow is set up. By using the Galerkin method in spatial domain and introducing new variables in time domain, the original integro-partial-differential system is reduced to a high dimensional differential system. The influence of aerodynamic pressure on the stability of viscoelastic cylindrical shells is investigated by various methods in nonlinear dynamics. It is found that the aero-viscoelastic cylindrical shell has two kinds of stable motions and two kinds of unstable motions.