STUDY ON RESPONSE CHARACTERISTICS OF A CLASS OF PIECEWISE SMOOTH NONLINEAR PLANAR MOTION SYSTEMS
-
摘要: 针对由一个线性子系统和一个非线性子系统构成的两自由度非自治分段光滑非线性平面运动系统的响应特性开展了研究. 该分段光滑非线性模型可用来确定对称转子/定子系统的主要碰摩响应, 且在反映非光滑系统典型特性上具有明显的特征:(1) 切换分界面是由两自由度坐标共同决定的一个幅值曲面;(2) 子系统周期解与分界面的擦碰, 不是发生在一个点上, 而是同时发生在解的所有点上;(3) 完整系统未发现由两子系统共同作用而产生的周期解. 因此, 对于该非光滑系统响应特性的研究, 很难直接利用目前有关非光滑系统平衡点和周期解分岔分析的方法. 为此, 尝试了根据子系统的响应特性, 划分出完整系统响应对分界面处切换的敏感区和非敏感区, 并针对非敏感区可由子系统解的特性求得完整系统的响应, 而针对敏感区通过子系统动力学特征的分析有助于解释完整系统响应的生成机制.Abstract: In this paper, the response characteristics of a two-degree-of-freedom non-autonomous piecewise smooth nonlinear system, which consists of linear and nonlinear subsystem, are investigated. The piecewise smooth system can be used to determine the most important responses of a rotor/stator rubbing systems, and possesses some following peculiar features: (1) the switching surface is defined by the two displacement coordinates of the system and is a magnitude surface in the state space; (2) the touch of the periodic solutions of subsystems with the switching surface occurs always simultaneously at all points of the solution to make it different from gazing bifurcations or phenomena in the usual nonsmooth systems; (3) there is no periodic solution formed through connection of trajectories from two subsystems. So some techniques developed for the bifurcation analysis of equilibriums or periodic solutions are not directly applicable to the system. Thus, according to the dynamical characteristics of subsystems, this paper tries to classify the parameter regions into the switching sensitive and insensitive regions. In this way, the responses of whole system in the switching insensitive regions can be obtained from the analysis of the responses of subsystems. For some responses of the whole systems in the switching sensitive regions, explanation is given for their occurrence based on the dynamical characteristics of subsystems.
-
Key words:
- piecewise smooth systems /
- planar motion /
- switch sensitivity /
- multi-stability /
- bifurcation
-
1 Leine RI, van Campen DH. Bifurcation phenomena in non-smooth dynamical Systems. European Journal of Mechanics A/Solids, 2006,25: 595-616 2 di Bernardo M, Nordmark A, Olivar G. Discontinuity-induced bifurcations of equilibria in piecewise smooth and impacting dynamical systems. Physica D, 2008, 237: 119-136 3 di Bernardo M, Budd C, Champneys A, et al. Bifurcations in nonsmooth dynamical systems. SIAM Review, 2008, 50(4): 629-701 4 Leine RI, Nijmeijer H. Dynamics and bifurcations of non-smooth mechanical systems. In: Lecture Notes in Applied and Computational Mechanics, Berlin: Springer-Verlag, 2004. 18 5 胡海岩. 分段线性系统动力学的非光滑分析. 力学学报,1996,28(4): 483-488 (Hu Haiyan. Nonsmooth analysis of dynamics of a piecewise linear system. Acta Mechanica Sinica,1996,28(4):483-488 (in Chinese)) 6 徐慧东,谢建华. 一类两自由度分段光滑线性系统的分岔与混沌. 振动工程学报,2008,21(3): 279-285 (Xu Huidong, Xie Jianhua. Bifurcation and chaos of a class of 2dof piecewise linear systems. Journal of Vibration Engineering, 2008,21(3): 279-285 (in Chinese)) 7 Jiang J, Ulbrich H. Stability analysis of sliding whirl in a nonlinear jeffcott rotor with cross-coupling stiffness coeffcients. Nonlinear Dynamics, 2001, 24(3): 269-283 8 Jiang J. Determination of the global responses characteristics of a piecewise smooth dynamical system with contact. Nonlinear Dynamics,2009, 57 (3): 351-361 9 高文辉, 郭旭, 江俊.基于胞参考点映射法对转子/定子碰摩响应 的全局分析.动力学与控制学报, 2011, 9(4): 363-367 (Gao Wenhui, Guo Xu, Jiang Jun. Study on the global response characteristics of a rotor/stator contact system through point mapping under cell reference method. Journal of Dynamics and Control, 2011, 9(4):363-367 (in Chinese)) 10 李绍龙,张正娣,吴天一等. 广义BVP 电路系统的振荡行为及 其非光滑分岔机理. 物理学报, 2012, 61(6): 060504 (Li Shaolong, Zhang Zhengti, Wu Tianyi, et al. Oscillating behavior and bifurcation mechanism of generalized BVP circuit. Journal of Chinese Physics, 2012, 61(6): 060504 (in Chinese)) -
点击查看大图
计量
- 文章访问数: 1363
- HTML全文浏览量: 45
- PDF下载量: 936
- 被引次数: 0
下载:
