Experiments on Chaotic Vibrations of a Simply Supported Circular Plate with Initial Deformation(<Special Issue>D & D 2008)

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  • MARUYAMA Shinichi
    Department of Mechanical System Engineering, Graduate School of Engineering, Gunma University
  • NAGAI Ken-ichi
    Department of Mechanical System Engineering, Graduate School of Engineering, Gunma University
  • HAYASHI Yusuke
    Department of Mechanical System Engineering, Graduate School of Engineering, Gunma University
  • YAMAGUCHI Takao
    Department of Mechanical System Engineering, Graduate School of Engineering, Gunma University

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  • 全周単純支持された初期変形を有する円板のカオス振動実験(<特集>D&D 2008)
  • 全周単純支持された初期変形を有する円板のカオス振動実験
  • ゼン シュウ タンジュン シジ サレタ ショキ ヘンケイ オ ユウスル エンバン ノ カオス シンドウ ジッケン

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Abstract

Experimental resuls are presented on chaotic vibrations of a simply supported circular plate with initial deformation. The plate is excited by lateral periodic excitation. In typical frequency range, non-periodic response is observed. The amplitude of response shows the irregular movement with amplitude modulation. The response is examined by the Fourier spectra, the maximum Lyapunov exponent and the Poincare projection. The response is found to be the chaotic response and that is generated from internal resonance condition of one to four. Time responses at the five points of the plate are measured simultaneously within long time interval. Applying the principal component analysis on the response of long time interval, it is found that three lower modes of vibration are generated in the chaos. The lowest mode of vibration contributes to the chaos dominantly. The second mode with one nodal diameter and the third mode with two nodal diameters contribute with small amount. The principal component is calculated with every short time intervals, the large amplitude of the chaotic response the contribution of the lowest mode of vibration predominantly. When the amplitude of the chaotic response decreases, the contribution of the lowest mode is decreased by 10 percent while the higher modes increase.

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