Nonlinear free vibration of isotropic plates with internal resonance

Ribeiro, P. and Petyt, M. (2000) Nonlinear free vibration of isotropic plates with internal resonance. International Journal of Non-linear Mechanics, 35, (2), 263-78. (doi:10.1016/S0020-7462(99)00013-X).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0020-7462(99)00013-X
Related URLs:
Keywords: Non-linear vibration; Plates; Internal resonance
Subjects: T Technology > TJ Mechanical engineering and machinery
Divisions : University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Dynamics
ePrint ID: 9937
Accepted Date and Publication Date:
Date Deposited: 03 Nov 2004
Last Modified: 31 Mar 2016 11:13

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