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The magneto-elastic internal resonances of rectangular conductive thin plate with different size ratios

journal contribution
posted on 2018-10-01, 00:00 authored by J Li, Y D Hu, Yanan WangYanan Wang
Based on the basic equations of electromagnetic elastic motion and the expression of electromagnetic force, the electromagnetic vibration equation of the rectangular thin plate in transverse magnetic field is obtained. For a rectangular plate with one side fixed and three other sides simply supported, its time variable and space variable are separated by the method of Galerkin, and the two-degree-of-freedom nonlinear Duffing vibration differential equations are proposed. The method of multiple scales is adopted to solve the model equations and obtain four first-order ordinary differential equations governing modulation of the amplitudes and phase angles involved via 1:1 or 1:3 internal resonances with different size ratios. With a numerical example, the time history response diagrams, phase portraits and 3-dimension responses of two order modal amplitudes are respectively captured. And the effects of initial values, thickness and magnetic field intensities on internal resonance characteristics are discussed respectively. The results also present obvious characteristics of typical nonlinear internal resonance in this paper.

History

Journal

Journal of mechanics

Volume

34

Issue

5

Pagination

711 - 723

Publisher

Cambridge University Press

Location

Cambridge, Eng.

ISSN

1727-7191

eISSN

1811-8216

Language

eng

Publication classification

C Journal article; C1 Refereed article in a scholarly journal

Copyright notice

2017, The Society of Theoretical and Applied Mechanics