Nonlinear free vibration of isotropic plates with internal resonance
Nonlinear free vibration of isotropic plates with internal resonance
The geometrically non-linear free vibration of thin isotropic plates is investigated using the hierarchical finite element method (HFEM). Von Kármán's non-linear strain–displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and the harmonic balance method (HBM), and the solutions are determined using a continuation method. The convergence properties of the HFEM and of the HBM are analyzed. Internal resonances are discovered. The variation of the plate's mode shape with the amplitude of vibration and during the period of vibration is demonstrated.
Non-linear vibration, Plates, Internal resonance
263-78
Ribeiro, P.
802ab1e9-46aa-446f-9ccc-db6fd25e5a78
Petyt, M.
741e8047-ace8-4003-b338-7e998d0303e5
2000
Ribeiro, P.
802ab1e9-46aa-446f-9ccc-db6fd25e5a78
Petyt, M.
741e8047-ace8-4003-b338-7e998d0303e5
Ribeiro, P. and Petyt, M.
(2000)
Nonlinear free vibration of isotropic plates with internal resonance.
International Journal of Non-Linear Mechanics, 35 (2), .
(doi:10.1016/S0020-7462(99)00013-X).
Abstract
The geometrically non-linear free vibration of thin isotropic plates is investigated using the hierarchical finite element method (HFEM). Von Kármán's non-linear strain–displacement relationships are employed and the middle plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and the harmonic balance method (HBM), and the solutions are determined using a continuation method. The convergence properties of the HFEM and of the HBM are analyzed. Internal resonances are discovered. The variation of the plate's mode shape with the amplitude of vibration and during the period of vibration is demonstrated.
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Published date: 2000
Keywords:
Non-linear vibration, Plates, Internal resonance
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Local EPrints ID: 9937
URI: http://eprints.soton.ac.uk/id/eprint/9937
PURE UUID: d00a9d70-59f5-4dab-a01e-02926fc53aaf
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Date deposited: 03 Nov 2004
Last modified: 15 Mar 2024 04:57
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Author:
P. Ribeiro
Author:
M. Petyt
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