Influence of the unilateral elastic base on the backbone curves of an imperfect cylindrical panel

This work evaluates the influence of a discontinuous unilateral elastic base and an initial geometrical imperfection on the nonlinear free vibration of cylindrical panels. The Donnell’s nonlinear shallow shell theory is considered to describe the cylindrical panel, then the equations are discretized by the Galerkin method. The unilateral elastic base is represented by the Signum function, and the Heaviside function describes the discontinuity of the elastic base. The results show the analysis of the nonlinear free vibrations of the cylindrical panel through the backbone curves, investigating the influence of the hypothesis of contact of the unilateral elastic base and the initial geometrical imperfection of the cylindrical panel. The modal solution employed has with five degree-of-freedom, being sufficient to describe the nonlinear softening behavior of the imperfection cylindrical panel in contact with the discontinuous unilateral elastic base. The numerical results reveal that the imperfect cylindrical panel in contact with unilateral elastic base presents less structural stiffness than in contact with bilateral elastic base, with decreasing the natural frequencies. In conclusion, the backbone curves are strongly influenced by discontinuous unilateral elastic base and the imperfections of the cylindrical panel.