Asymmetric non-linear forced vibrations of free-edge circular plates. Part 1: Theory - ENSTA Paris - École nationale supérieure de techniques avancées Paris Access content directly
Journal Articles Journal of Sound and Vibration Year : 2002

Asymmetric non-linear forced vibrations of free-edge circular plates. Part 1: Theory

Cyril Touzé
Olivier Thomas
Antoine Chaigne
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Abstract

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 Kàrmàn 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 $\omega_n$ of one asymmetric mode of the plate. Thus, the vibration is governed by the two degenerated modes corresponding to $\omega_n$, 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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Dates and versions

hal-00830697 , version 1 (17-03-2016)

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Cyril Touzé, Olivier Thomas, Antoine Chaigne. Asymmetric non-linear forced vibrations of free-edge circular plates. Part 1: Theory. Journal of Sound and Vibration, 2002, 258 (4), pp.649-676. ⟨10.1006/jsvi.2002.5143⟩. ⟨hal-00830697⟩

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