CAJ | 학술논문

以一类两自由度含间隙弹性碰撞系统为研究对象,建立了弹性碰撞系统的力学模型,利用 Runge-Kutta 数值模拟算法,分析了系统在低频下单周期多碰撞周期运动及颤振运动特性,并揭示了p/1周期运动的 saddle-node分岔和 Grazing分岔。研究结果表明：随着激振频率的递减,p/1运动的碰撞次数p因 Grazing 分岔而逐一增加；随着激振频率的增加,p/1运动的碰撞次数p因 saddle-node分岔而逐一减少；p/1和(p+1)/1周期运动间存在 sad-dle-node分岔和Grazing分岔的频率迟滞和吸引子共存现象。在低频工况下,p/1运动的碰撞次数p足够大时,系统呈现出颤振特性,得出了系统由1/1周期运动到颤振的转迁规律。
이일류량자유도함간극탄성팽당계통위연구대상,건립료탄성팽당계통적역학모형,이용 Runge-Kutta 수치모의산법,분석료계통재저빈하단주기다팽당주기운동급전진운동특성,병게시료p/1주기운동적 saddle-node분차화 Grazing분차。연구결과표명：수착격진빈솔적체감,p/1운동적팽당차수p인 Grazing 분차이축일증가；수착격진빈솔적증가,p/1운동적팽당차수p인 saddle-node분차이축일감소；p/1화(p+1)/1주기운동간존재 sad-dle-node분차화Grazing분차적빈솔지체화흡인자공존현상。재저빈공황하,p/1운동적팽당차수p족구대시,계통정현출전진특성,득출료계통유1/1주기운동도전진적전천규률。
The dynamic model of a two-degree-of-freedom system with clearance and soft impacts is considered.The multi-impact motions of one excitation period and chattering-impact characteris-tics of the system are analyzed by Runge-Kutta numerical simulation algorithm,and furthermore Saddle-node and Grazing bifurcations between p/1 motions are revealed exactly.The research re-sults show that a series of Grazing bifurcations occur with decreasing frequency so that the impact number p of p/1 motions correspondingly increases one by one;a series of Saddle-node bifurca-tions occur with increasing frequency so that the impact number p of p/1 motions correspondingly decreases one by one,and there exists frequency hysteresis and multiple attractors coexistence be-tween p/1 and (p+1)/1 motions.In the low exciting frequency case,the impact number p of p/1 motions becomes big enough and chattering-impact characteristics will be appearing.The transi-tion law from 1/1 motion to chattering-impact motion is summarized explicitly.