Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part I: Stability

Amabili, Marco; Pellicano, Francesco; Paı̈doussis, M.P.

doi:10.1006/jsvi.1999.2255

Cited by 169 publications

(146 citation statements)

References 26 publications

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“…motion [42,43,44]. This is also why in Table 1, eigenmodes are presented by increasing order of the frequencies, except the last two (axisymmetric), which have significantly larger eigenfrequencies: asymmetric modes in between have not been reported in the table.…”

Section: Numerical Detailsmentioning

confidence: 85%

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Touzé

Thomas

Amabili

2011

International Journal of Non-Linear Mechanics

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The transition from periodic to chaotic vibrations in free-edge, perfect and imperfect circular plates, is numerically studied. A pointwise harmonic forcing with constant frequency and increasing amplitude is applied to observe the bifurcation scenario. The von Kármán equations for thin plates, including geometric nonlinearity, are used to model the large amplitude vibrations. A Galerkin approach based on the eigenmodes of the perfect plate allows discretizing the structure. The resulting ordinary-differential equations are numerically integrated. Bifurcation diagrams of Poincaré maps, Lyapunov exponents and Fourier spectra analysis reveals the transitions and the energy exchange between modes. The transition to chaotic vibration is studied in the frequency range of the first eigenfrequencies. The complete bifurcation diagram and the critical forces needed to attain the chaotic regime are especially adressed. For perfect plates, it is found that a direct transition from periodic to chaotic vibrations is at hand. For imperfect plates displaying specific internal resonance relationships, the energy is first exchanged between resonant modes before the chaotic regime. Finally, the nature of the chaotic regime, where a high-dimensional chaos is numerically found, is questioned within the framework of wave turbulence. These numerical findings confirm a number of experimental observations made on shells, where the generic route to chaos displays a quasiperiodic regime before the chaotic state, where the modes, sharing internal resonance relationship with the excitation frequency, ap- *

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Section: Numerical Detailsmentioning

confidence: 85%

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Touzé

Thomas

Amabili

2011

International Journal of Non-Linear Mechanics

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“…For a formulation based on a stress function, the in-plane boundary conditions are satisfied on the average by introducing the following conditions, as justified, for example, in [20,21,22,23,24]…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…This leads to a six-degrees-of-freedom reduced order model. This modal expansion satisfies the out-of-plane boundary conditions (10) and includes the basic vibration mode, the companion mode and four axi-symmetric modes and has been thoroughly tested in [20,21,24].…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…(9), and by solving the resulting partial differential equation together with the relevant boundary and continuity conditions. The homogeneous part of the stress function can be written as (Amabili et al, 1999): F and w(x, , t) into the equation of motion, Eq. (8), and applying the Galerkin method, a set of six non-linear ordinary differential equations is obtained in terms of the time-dependent modal amplitudes,  i (t).…”

Section: Mathematical Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

Prado¹,

Amabili²,

Gonçalves³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. In this work the influence of geometry, load and material properties on the nonlinear vibrations of a simply supported viscoelastic circular cylindrical shell subjected to lateral harmonic load is studied. Donnell's non-linear shallow shell theory is used to model the shell, assumed to be made of a Kelvin-Voigt material type, and a modal solution with six degrees of freedom is used to describe the lateral displacements. The Galerkin method is applied to derive a set of coupled non-linear ordinary differential equations of motion.Obtained results show that the viscoelastic dissipation parameter has significant influence on the instability loads and resonance curves.

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“…Amabili et al (1999 performed a complete study of the nonlinear stability and forced response of simply supported circular cylindrical shells with #ow by using Donnell's nonlinear shallow-shell theory. In particular, they have shown for the "rst time that the stability of a shell conveying #uid predicted by linear theory can be largely nonconservative and that the stability limit must be calculated by using a nonlinear shell theory.…”

Section: Introductionmentioning

confidence: 99%

Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass. Part Ii: Shells Containing or Immersed in Axial Flow

Amabili

Garziera

2002

Journal of Fluids and Structures

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Non-Linear Dynamics and Stability of Circular Cylindrical Shells Containing Flowing Fluid. Part I: Stability

Cited by 169 publications

References 26 publications

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates

Geometry Effects on the Nonlinear Oscillations of Viscoelastic Cylindrical Shells

Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass. Part Ii: Shells Containing or Immersed in Axial Flow

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