Comparative analysis of dynamic stability of cylindrical and conical shells under periodic axial compression

A comparative analysis of the dynamic stability cylindrical and conical shells with same geometric mechanical characteristics under periodic uniformly distributed axial compression was presented. The study steady vibrations thin elastic based on joint use method curvilinear grids, projection parameter continuation combined Newton–Kantorovich method. Geometrically nonlinear relations theory are formulated basis vector approximation displacements function in general coordinate system tensor form satisfy Kirchhoff-Love hypothesis. discretization differential equations forced direction generating using grids carried out. components elements displacement vectors middle surface circular directionare approximated by trigonometric series. Reduction number generalized coordinates discrete model performed Bubnov-Galerkin reduction transition from ordinary to a algebraic made. construction mathematical according Floquet's criterion for loss equality zero determinant matrix linearized Lyapunov theorem. frequencies modes natural boundary conditions performed. Nonlinear due were studied. critical values load corresponding forms shell range lower their obtained.