Aeroelastic Stability of a Cylindrical Shell of Linearly Varying Thickness

Abstract

For the first time, the equations of aeroelastic stability of a composite cylindrical shell of linearly varying thickness are obtained on the basis of the bending theory of orthotropic shells under loading with axial forces and supersonic gas flow. The solution to the equations is sought in the form of trigonometric series along the axial coordinate. The problem is reduced to an infinite system of algebraic equations by the Bubnov–Galerkin method. The characteristic equation obtained is approximated by the Lagrange polynomial, the stability of which is investigated using the Routh–Hurwitz criterion. By a numerical example, the effect of the thickness gradient, structural damping, and axial force on the critical velocity when flow by a supersonic gas around а shell of linearly varying thickness is shown. The refinement of the results of calculations carried out with the model developed amounted to almost 35% for the critical velocities as compared to those found from the model for a shell with an average thickness, which evidences the urgency of the problem solved for weight perfection of aircrafts. The approach proposed significantly extends the range of problems to be solved and allows calculating the aeroelastic stability of orthotropic cylindrical shells of linearly varying thickness in the flow around by the supersonic gas flow.