%0 Journal Article
%T ANALYSIS TO MOTIONS OF A TWO-DEGREE-OF- FREEDOM VIBRO-IMPACT SYSTEM<br>一类双自由度碰振系统运动分析
%A Li Qunhong Lu Qishao
%A <br>李群宏
%A 陆启韶
%J 力学学报
%D 2001
%I 
%X An undamped two-degree-of-freedom vibro-impact system with a harmonic excitation is under consideration based on the Poincar 'e map in this paper. In general case, due to the complexity of this kind of problems, it is difficult to give a satisfied theoretical analysis on the issues of periodic impact motions, bifurcations and chaos for multi-degree-of-freedom dynamical systems. So far, most of achievements are obtained for the one-degree-of-freedom vibro-impact systems with the property of piecewise linear by distinguished scholars, for instance, Shaw, Whiston and Nordmark, etc. In addition, a few cases have been studied for the piecewise linear vibro-impact systems with two degrees of freedom provided that there is a fixed rigid constraint boundary. Here we take into account a situation in which two oscillators move relatively under the harmonic excitation and the contact surface is rigid but unknown before impact. Our attention is paid to single impact period- n motions which have an impact occurred for every n times of the external excitation period. By a great deal of computation, we get an existent criterion of single impact period- n motions in the above piecewise linear impact system. The criterion is governed by a second order algebraic equation that is clearly solvable. This means that it is possible that there exist periodic impact motions even if the impact border is uncertain in the system with rather complicated impact law since two oscillators are involved in impact events. Moreover, the stability of periodic motions is studied and the corresponding formula is derived from the Poincar 'e map of the system discussed. The complex form of the derived stability criterion prevents us from developing more analytical results except the numerical simulation. Finally, it is shown that our conclusions are valid through the numerical simulation. And other motion modes are explored when the criterion for single impact period- n subharmonic motions is not available.
%K vibro-impact
%K subharmonic motion
%K Poincar 'e map
%K existent criterion
%K stability<br>碰撞振动
%K 次谐运动
%K Pincare映射
%K 存在判据
%K 稳定性
%K 机械振动
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=5D344E2AD54D14F8&jid=4100DA4A1A3BA1B0CE5AD99AE1DFB420&aid=BF224BE5A644E229&yid=14E7EF987E4155E6&vid=27746BCEEE58E9DC&iid=B31275AF3241DB2D&sid=FE17D37BFC90FA6B&eid=CFBDB06850C21CC6&journal_id=0459-1879&journal_name=力学学报&referenced_num=17&reference_num=20