Multi-mode nonlinear vibration and large deflection of symmetrically laminated imperfect spherical caps on elastic foundations

A dynamic nonlinear theory for laminated spherical caps is developed with the use of Hamilton's principle. The effects of shear deformation, rotatory inertia, geometrically initial imperfection and elastic foundation are included in the analysis. The governing equations are expressed in terms of the transverse displacement, stress function and rotation. The solution of a multi-mode Fourier-Bessel series is formulated for the nonlinear flexural free vibration of symmetrically laminated moderately thick spherical caps with flexible supports. The resulting equations for time functions are solved by the method of harmonic balance. The corresponding large deflection problem is treated as a special case. The effects of geometric imperfections and of the elastic foundation are investigated. Numerical results are compared with available data.