和差調波振動の共振曲線と安定性について

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  • On the Response Curves and the Stability of "Summed and Differential Harmonic" Oscillations
  • ワサチョウハ シンドウ ノ キョウシン キョクセン ト アンテイセイ ニ ツイテ

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In the present paper, the authors obtain theoretically the response curves of summed and differential harmonic oscillations induced by symmetrical and unsymmetrical nonlinearities of spring forces, and they investigate the influences of nonlinearities and damping forces of those vibrations. Futher the stability criteria of vibrations are analytically studied. The conclusions obtained are as follows : (1) The characteristics of summed and differential harmonic oscillations are analogous to those of sub-harmonic oscillations of order 1/2 and 1/3. (2) There are the critical values of damping coefficients, and the summed and differential harmonic oscillations cannot take place, when the magnitudes of damping are larger than these critical values. (3) The loci of vertical tangency of the response curves divide the response curves into two parts, and the upper parts of the loci are the stable range, the lower unstable.

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