非線形ばね特性をもつ三自由度係数励振系の内部共振現象 : 第1報,固有振動数間にlp_i+mp_j=np_kの関係がある場合

抄録

In a parametrically excited system whose natural frequencies are p_i, p_j, p_k, and the parametric excitation frequency is Ω, an oscillation of a subharmonic type occurs when the relation p_i∼_- Ω/2 holds and that of a combination type occurs when the relation p_i + p_j ∼_- Ω/2 holds. When the restoring forces are linear, these oscillations are unstable oscillations. But it is known that, in a nonlinear system, the nonlinearity modifies the growth of the unstable vibration and results in the steady oscillation with finite amplitude. In this paper, the internal resonance phenomena in such a system with nonlinear spring characteristics are investigated. Especially, we treat the case where the relation lp_i + mp_j = np_k holds but each natural frequency is not an integer multiple of another natural frequency. By theoretical analysis, we clarified the followings : the kinds of parametric excitation terms and nonlinear terms which have an influence on oscillations ; induction of oscillation due to internal resonance ; occurrence of the almost periodic oscillations ; and so on.