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ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY

✍ Scribed by C. TOUZÉ; O. THOMAS; A. CHAIGNE

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
903 KB
Volume
258
Category
Article
ISSN
0022-460X

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✦ Synopsis

In this article, a detailed study of the forced asymmetric non-linear vibrations of circular plates with a free edge is presented. The dynamic analogue of the von K" a arm" a an equations is used to establish the governing equations. The plate displacement at a given point is expanded on the linear natural modes. The forcing is harmonic, with a frequency close to the natural frequency o kn of one asymmetric mode of the plate. Thus, the vibration is governed by the two degenerated modes corresponding to o kn ; which are one-to-one internally resonant. An approximate analytical solution, using the method of multiple scales, is presented. Attention is focused on the case where one configuration which is not directly excited by the load gets energy through non-linear coupling with the other configuration. Slight imperfections of the plate are taken into account. Experimental validations are presented in the second part of this paper.

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