Asymmetric Vibrations and Chaos in Spherical Caps under Uniform Time-varying Pressure Fields

Abstract

This paper presents a study on nonlinear asymmetric vibrations in shallow spherical caps under pressure loading. The Novozhilov’s nonlinear shell theory is used for modelling the structural strains. A reduced-order model is developed through the Rayleigh-Ritz method and Lagrange equations. The equations of motion are numerically integrated using an implicit solver. The bifurcation scenario is addressed by varying the external excitation frequency. The occurrence of asymmetric vibrations related to quasi-periodic and chaotic motion is shown through the analysis of time histories, spectra, Poincaré maps, and phase planes.