Nonlinear resonance curves of a cylindrical panel with unilateral contact of a discontinuous elastic base

Resumo

The aim of this work is to analyze the influence of a discontinuous unilateral elastic base and an initial
geometrical imperfection on the nonlinear vibrations of a simply supported cylindrical panel. The cylindrical panel
is described by the nonlinear shallow shell theory of Donnell and discretized by the Galerkin method, using a
reduced order model which is obtained by a perturbation method. The discontinuous elastic base model is described
by a Heaviside function and the unilateral contact is defined by the Signum function. The results show the dynamic
analysis of the cylindrical panel through the backbone curves, bifurcation diagrams, phase portraits and resonance
curves to understanding the influence of the discontinuous unilateral elastic base and the initial geometrical
imperfection of the cylindrical panel. An efficient modal solution with two degree-of-freedom is sufficient to
describe the nonlinear softening behavior of the cylindrical panel with a discontinuous unilateral elastic base. The
influence of the unilateral elastic base and the initial geometrical imperfection on the dynamic stability of the
cylindrical panel is demonstrated in the resonance curves, phase planes, Poincaré mappings and bifurcation
diagrams, where it is possible to identify important changes in the stable and unstable regions of the resonance
curves when compared with a cylindrical panel with a discontinuous bilateral elastic base.