Three–dimensional axisymmetric vibrations of orthotropic and cross–ply laminated hemispherical shells



Free vibration of orthotropic and cross–ply laminated hemispherical shells using elasticity approach is studied. The Navier type equations are transformed into partial differential equations with constant coefficients in radial direction, assuming that the ratio of the thickness to mean radius of each lamina of the shell is small and hence can be neglected with respect to unity. The partial differential equations are reduced to ordinary differential equations, by applying Galerkin method, using Legendre polynomials along the meridian direction. The resulting ordinery differential equations are solved exactly for each layer. Connecting all of the exact solutions by means of appropriate continuity conditions and by using a method of successive approximation the solution of the problem is achieved. Convergence tests have been carried out to demonstrate the veracity of the approach. Numerical results are presented and compared with the latest results found in the literature.