Free vibration analysis of laminated orthotropic spherical shells

Analytical solutions are presented for the free vibration of laminated orthotropic spherical shells. The analysis is based on the application of the Chebyshev-Galerkin spectral method for the evaluation of free vibration frequencies and mode shapes. The eigenvalue problem is defined in terms of five equations of motion in terms of the meridional coordinate, the circumference variation of the displacements being represented in a Fourier series. Numerical results are presented to show the validity and accuracy of the proposed method. Results of parametric studies for laminated annular spherical shells with different orthotropic ratios, opening angles, lamination sequences and shear deformation are also presented.