非線形ばね特性をもつ二自由度係数励振系の内部共振現象 : 第1報,分数形係数励振振動について

概要

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In a parametrically excited with linear spring characteristics (p_i, p_j : natural frequency, Ω : frequency of parametric excitation), unstable vibrations occur when the relations p_i≒Ω/2 and p_i+p_j≒Ω hold. We call the former a subharmonic type and the latter a combination type. In a nonlinear system, the nonlinearity modifies the growth of unstable vibrations and results in the steady oscillation with finite amplitude. In the present paper, we investigate the effects of internal resonance on the parametrically excited oscillation of subharmonic type. We study the unstable region at p_i≒Ω/2 and p_2≒Ω in a two-degree-of-freedom system where p_1 : p_2≒1 : 2 or 1 : 3 holds. It is clarified that the oscillations of these four cases have different characteristics concerning the following points : kinds of influential coefficients of parametric excitation terms and nonlinear terms, shapes of resonance curves, induction of oscillation due to internal resonance, occurrence of almost periodic oscillations, and so on.
一般社団法人日本機械学会の論文
1986-02-25