NONLINEAR VIBRATION AND BUCKLING ANALYSIS OF LAMINATED SHALLOW SPHERICAL-SHELLS WITH HOLES

The static and dynamic non-linear axisymmetric response of a shallow s pherical shell with a circular opening at the apex has been investigat ed The shell consists of a number of radially orthotropic layers perfe ctly bonded together but symmetrically laminated. The governing equati ons are expressed in terms of the transverse displacement, rotation an d stress function. The effects of transverse shear and rotatory inerti a are included in the analysis. The shell edge is elastically restrain ed against rotation and in-plane displacement. The vanishing of the ro tation and in-plane displacement at the opening are assumed. A Fourier -Bessel series solution is formulated for the postbuckling and large a mplitude free vibration of the shell. The Galerkin procedure furnishes a set of non-linear ordinary differential equations for time function s which are solved by the method of harmonic balance. Numerical result s in postbuckling response and non-linear free vibration are presented for various boundary conditions, ratios of base radius to thickness, and shell rise to thickness, and numbers of layers. The results are al so compared with available darn.