Nonlinear dynamics of thin plate subject to multiple force excitations

ZHANG Dan-wei,HUANG Jian-liang

Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (23) : 174-179.

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PDF(1480 KB)
Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (23) : 174-179.

Nonlinear dynamics of thin plate subject to multiple force excitations

  • ZHANG Dan-wei,HUANG Jian-liang
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Abstract

The Incremental Harmonic Balance (IHB) method was used to analyze nonlinear dynamics of rectangular thin plate with four simply supported sides, subjected to the external two-tone transverse harmonic excitation. Based on the vibration differential equation of thin plate, the non-dimensional Duffing nonlinear forced vibration equation was deduced by using Galerkin method. Introducing multiple time variables defined as  , in which   were the nonlinear frequencies of responses incommensurable with one another, corresponding calculation process of IHB method was derived. As a numerical example, time histories diagrams, spectrum diagrams, phase diagrams and Poincaré section were presented by IHB method with different excitations, and quasi-periodic motions of the plate which undergo the external multi-excitations were obtained. Meanwhile the results obtained from the IHB method are in good agreement with the results obtained from the numerical integration method.

Key words

rectangular thin plate / nonlinear vibration / Incremental Harmonic Balance method / multiple force excitations / quasi-periodic motion

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ZHANG Dan-wei,HUANG Jian-liang. Nonlinear dynamics of thin plate subject to multiple force excitations[J]. Journal of Vibration and Shock, 2016, 35(23): 174-179

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