Nonlinear axisymmetric flexural vibration of spherical shells

Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.