An alternative procedure for the non-linear vibration analysis of fluid-filled cylindrical shells

• Published in: Nonlinear dynamics 2011-11, Vol.66 (3), p.303-333
• Main Authors: Silva, Frederico M. A., Gonçalves, Paulo B., del Prado, Zenón J. G. N.
• Format: Article
• Language: English
• Subjects: Automotive Engineering; Axial loads; Bifurcations; Classical Mechanics; Control; Cylindrical shells; Dimensional stability; Dynamic stability; Dynamic tests; Dynamical Systems; Dynamics; Engineering; Equations of motion; Equilibrium equations; Flow theory; Galerkin method; Lateral pressure; Lateral stability; Linear vibration; Liquid filled shells; Mathematical models; Mechanical Engineering; Nonlinear analysis; Nonlinear dynamics; Nonlinear equations; Nonlinearity; Original Paper; Parametric analysis; Perturbation methods; Potential flow; Proper Orthogonal Decomposition; Reduced order models; Safety; Shallow shell equations; Shallow shells; Shell stability; Shells; Vibration; Vibration analysis
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-011-0037-z

Using Donnell non-linear shallow shell equations in terms of the displacements and the potential flow theory, this work presents a qualitatively accurate low dimensional model to study the non-linear dynamic behavior and stability of a fluid-filled cylindrical shell under lateral pressure and axial loading. First, the reduced order model is derived taking into account the influence of the driven and companion modes. For this, a modal solution is obtained by a perturbation technique which satisfies exactly the in-plane equilibrium equations and all boundary, continuity, and symmetry conditions. Finally, the equation of motion in the transversal direction is discretized by the Galerkin method. The importance of each mode in the proposed modal expansion is studied using the proper orthogonal decomposition. The quality of the proposed model is corroborated by studying the convergence of frequency–amplitude relations, resonance curves, bifurcation diagrams, and time responses. The parametric analysis clarifies the influence of the lateral and axial loads on the non-linear vibrations and stability of the liquid-filled shell. Finally, the global response of the system is investigated in order to quantify the degree of safety of the shell in the presence of external perturbations through the use of bifurcation diagrams and basins of attraction. This allows one to evaluate the safety and dynamic integrity of the cylindrical shell in a dynamic environment.