三自由度防振支持系のNonlinear Normal Modes : 内部共振現象の存在する場合(機械力学,計測,自動制御)

概要

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The new methods are presented for detecting Nonlinear Normal Modes (NNMs), which are defined as synchronous periodic motions of nonlinear systems, in modern analysis of nonlinear dynamics. In this work, NNMs in a three-degree-of-freedom (3 d. o. f.) vibration isolating systems, i.e., the vertical, horizontal and rotating vibrations, with '2-1-1' internal resonance are examined using this method as the examples of Non Similar Modes. The equations of motion of the 3 d. o. f. vibration system considering geometric nonlinearities are derived, and NNMs are investigated in the conservative nonlinear system. A forced oscillation of the nonconservative nonlinear system is analyzed with the method of multiple scales, in order to investigate the angular frequencies of excitation vs. amplitudes and phase characteristics. Moreover, the response curves are obtained analytically. Furthermore a 3 d. o. f. experimental equipment was set up, and the presence of bifurcation in the internal resonance was experimentally verified with the primary resonant excitation.
社団法人日本機械学会の論文
2002-07-25