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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Multi-Modal Non-linear Free Vibration of Thin Isotropic Circular Plates
verfasst von : M. Haterbouch, P. Ribeiro, R. Benamar
Erschienen in: III European Conference on Computational Mechanics
Verlag: Springer Netherlands
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The large-amplitude periodic free axisymmetric vibration of clamped immovable thin isotropic circular plates is investigated using the energy method and a multimode approach. 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 derived by applying Lagrange’s equations. Using the harmonic balance method (HBM), the equations of motion are converted into a non-linear algebraic form and are solved by a continuation method. Interesting results for the plate’s fundamental mode shape such as the occurrence of internal resonance, resulting in a complicated backbone curve, and the variation of the mode shape with the amplitude of vibration and during the period of vibration are obtained.