Abstract
In this work, the nonlinear dynamic response of a shallow spherical cap subjected to a time-dependent pressure load is analyzed. The Novozhilov’s nonlinear thin shell theory is used to express the strain-displacement relations, geometric imperfections are considered. Using the Rayleigh-Ritz method, the displacement fields are expanded using a mixed series: Legendre polynomials are considered in the azimuthal direction and harmonic functions in the circumferential one. The dynamic model is derived by using the Lagrange equations. The response of a homogeneous shell, made of isotropic material, clamped at its ends, and subjected to an external pressure load is investigated: using the continuation software AUTO, the bifurcation analysis of equilibrium points and periodic responses has been performed. The model is validated by means of comparison with the existing results in literature for spherical shells having a circular base, in particular with models developed through the Marguerre’s theory.
