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

Abstract : 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 non-linearity, are used to model the large-amplitude vibrations. A Galerkin approach based on the eigenmodes of the perfect plate allows discretizing the model. The resulting ordinary-differential equations are numerically integrated. Bifurcation diagrams of Poincaré maps, Lyapunov exponents and Fourier spectra analysis reveal 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 addressed. 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, appear in the response.
Complete list of metadatas

Cited literature [54 references]  Display  Hide  Download

https://hal-ensta-paris.archives-ouvertes.fr//hal-01134807
Contributor : Cyril Touzé <>
Submitted on : Monday, March 14, 2016 - 11:39:38 AM
Last modification on : Wednesday, September 25, 2019 - 11:06:03 AM
Long-term archiving on : Sunday, November 13, 2016 - 5:46:54 PM

File

2011_Transichaos.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Cyril Touzé, Olivier Thomas, Marco Amabili. Transition to chaotic vibrations for harmonically forced perfect and imperfect circular plates. International Journal of Non-Linear Mechanics, Elsevier, 2011, 46 (1), pp.234-246. ⟨10.1016/j.ijnonlinmec.2010.09.004⟩. ⟨hal-01134807⟩

Share

Metrics

Record views

142

Files downloads

277