A hierarchical formulation of the state-space Levy's method for vibration analysis of thin and thick multilayered shells

The state-space approach in conjunction with the Levy's method is used to solve exactly the free vibration problem of specially orthotropic multilayered cylindrical and spherical panels. A hierarchical formulation is presented to build the matrices of the method from small elementary blocks which are invariant with respect to the order and typology of the kinematic shell theory. As a result, the analytical effort to derive the governing equations is minimized and a large number of Levy-type solution based on low to high order, equivalent single-layer or layerwise theories, can be generated within the same mathematical framework. Thereby, the refinement of the two-dimensional shell model can be tailored according to the thickness ratio and the degree of anisotropy of the problem under study and the desired accuracy. Some illustrative results on both thin and thick, laminated and sandwich panels with various boundary conditions are presented and discussed to show the potential of the formulation.