- The dynamic stability of thin, laminated cylindrical shells under combined static and periodic axial forces is studied using Love's classical theory of thin shells. A normal-mode expansion of the equations of motion yields a system of Mathieu-Hill equations. Bolotin's method is then employed to obtain the dynamic instability regions. The present study examines the dynamic stability of antisymmetric cross-ply circular, cylindrical shells of different lamination schemes. The effect of the magnitude of the axial load on the instability regions is also examined. 1998 Elsevier Science Ltd. All rights reserved.