ヒステリシス·ループの履歴特性をもつ2自由度ばね-質量系の定常衝突振動解析

摘要

二つの弾性体が互いに弾性衝突する2自由度系の衝rn突振動は衝突加工機などに応用されており，加工機のrn制振や最適衝撃条件の設定など設計上の観点から重要rnであり，衝突による応答変位や衝突に伴う反発力を定rn量的に解析する必要がある．しかし衝突振動はrn高速で，極めて短時間に衝突という比較的大きな非線rn形性を有する振動系で，一般的な解析結果から厳密にrn応答の推測をするのは困難である．したがってより合rn理的な衝突加工機の設計は個々の実例についてある程rn度厳密に解析する必要がある．2自由度ばね-質量系rnの場合は二つの質量体を有するので，これらが互いにrn弾性衝突するときの衝突間げきが一定ではなく，新たrnに変動間げきを考慮に入れた解析をしなければならなrnい．%The collision vibration is widely applied to the impact machining device since accurately large energy is comparatively obtained. It is necessary to quantitatively analyze response vibration and restitution force by collision for design of the impact machining device. As an example of basic investigation, this paper deals with impact vibration in a spring-mass system for two-degree of freedom excited by periodic force with arbitrary functions. The analytical model is steady impact vibration for two-degree of freedom having two masses subjected to an exciting vibration. Then the restitution force, which has characteristics of an unsymmetric piecewise-linear system with hysteresis loop, collides elastically with another mass when amptitude of the mass exceeds than the clearance. In order to analyze the resulting vibration for the main resonance, the Fourier series method is applied to obtain an exact solution for response vibration. The numerical calculation is performed to obtain the resonance curves. The numerical results show effects of the stiffness of the clampted spring and the amplitude of excitation on the resonance curves.