Nonlinear Vibrations of a Shallow Spherical Cap Under Pressure Loading

Abstract

Abstract The nonlinear vibrations of shallow spherical caps, under the action of static and fluctuating pressure, are studied. A meshless method based on the Novozhilov’s nonlinear thin shell theory is considered to reduce the partial differential equations (PDEs) to a set of ordinary differential equations (ODEs): the displacement fields are expanded though a mixed series of Legendre polynomials and harmonic functions in the meridional and circumferential directions respectively. The ODEs are obtained by taking advantage from the Lagrange equations and are analysed using continuation and direct integration techniques. Results show that nonlinear interactions can result in the activation of non-symmetric vibrational states characterized by weakly chaotic features.