Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Influence of a non-continuous and unilateral elastic base on the nonlinear vibrations of a cylindrical panel
Submission Author:
Frederico Martins Alves da Silva , GO , Brazil
Co-Authors:
Jordana Morais, Frederico Martins Alves da Silva
Presenter: Jordana Morais
doi://10.26678/ABCM.COBEM2023.COB2023-1468
Abstract
Cylindrical panels are structural elements that have applications in many engineering fields as civil, aerospatial, and mechanical engineering, among others. Generally, to prescribe their behavior and stability under dynamic loads, the mathematical model must consider their geometric nonlinearities and contact with an elastic medium. Thus, the objective of this work is to investigate the influence of a non-continuous, unilateral elastic base and an initial geometric imperfection on the nonlinear vibrations of a simply supported cylindrical panel. The cylindrical panel is described by the Donnell’s nonlinear shallow shell theory and is discretized using the Galerkin method. To reduce the set of the discretized equations of the dynamical system, a perturbation method is employed to derive a reduced-order model. The non-continuous elastic base model is represented by a Heaviside function, and the unilateral contact is defined using the Signum function. To provide a thorough analysis, the study presents a dynamic analysis of the cylindrical panel through backbone curves, bifurcation diagrams, phase portraits, and resonance curves. These results provide a comprehensive understanding of the impact of the non-continuous, unilateral elastic base and the initial geometric imperfection on the cylindrical panel. A two-degree-of-freedom efficient modal solution is employed to sufficiently describe the nonlinear softening behavior of the cylindrical panel. The numerical results reveal that the non-continuous, unilateral elastic base and the initial geometric imperfection have significant effects on the dynamic stability of the cylindrical panel, showing some Neimark-Sacker bifurcation points in the resonance curves. Moreover, the stable and unstable regions of the resonance curves exhibit important changes when compared with a cylindrical panel featuring a non-continuous, bilateral elastic base. In conclusion, this study provides valuable insights into the effects of non-continuous, unilateral elastic bases and initial geometric imperfections on the nonlinear vibrations of simply supported cylindrical panels.
Keywords
Cylindrical panel, nonlinear dynamics, unilateral contact, elastic base
