Summary
Nonlinear vibrations of a homogeneous, isotropic, and shallow spherical caps under a harmonic pressure field are studied. The problem is addressed using a semi-analytical method based on Novozhilov's nonlinear shell theory. The partial differential equations (PDEs) are reduced to a set of ordinary differential equations (ODEs) through the Rayleigh-Ritz approach and Lagrange's equations. The resulting set of equations is numerically solved using both continuation techniques and direct integration. The results highlighted the activation of non-symmetric vibrational states, with the presence of multiple bifurcations and chaotic oscillations.
