Aeroelastic stability of a cylindrical shell of linearly varying thickness

For the first time, the aeroelastic stability equations of a composite cylindrical shell of linearly varying thickness are obtained on the basis of the bending theory of orthotropic shells for a shell subjected to axial forces and supersonic gas flow. The solution of the equations is assumed of the form of a trigonometric series in the axial coordinate. The problem is reduced to an infinite system of algebraic equations by the Bubnov-Galerkin method. The obtained characteristic equation is approximated by the Lagrange polynomial, whose stability is investigated with the use of the Routh-Hurwitz criterion. As a numerical example, the effect of the thickness gradient, structural damping and axial force on the critical velocity for a composite shell of linearly varying thickness in supersonic gas flow is shown. The refinement in the value of the critical velocity resulting from the use of the suggested model is about 35% as compared to the results for a shell of averaged constant thickness. This indicates the relevance of this model for aircraft weight optimization. The suggested approach expands the range of problems to be solved and allows for the analysis of the aeroelastic stability for orthotropic cylindrical shells of linearly varying thickness in supersonic gas flow.