横纵激励下几何非线性复合材料层合梁的混沌同步  

Chaotic synchronization of a geometric nonlinear composite beam under horizontal-vertical excitations

作　　者：王龙飞[1] 韩志军[1] 闫晓鹏[1] 路国运[2] 

机构地区：[1]太原理工大学力学学院,太原030024 [2]太原理工大学建筑与土木工程学院,太原030024

出　　处：《振动与冲击》2016年第9期28-31,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(11372209);山西省自然科学基金(2013011005-1)

摘　　要：基于里兹-伽辽金法,将考虑几何非线性的一端固支一端夹支复合材料层合梁的控制方程简化为典型的Duffing方程;引入了Duffing-Van Der Pol系统,通过两种系统的分岔图说明了它们共同达到混沌时的参数值;通过广义投影同步法,实现了Duffing系统和Duffing-Van Der Pol系统的精确同步,得到了实现两种系统同步的控制器;分别将两种系统通过Matlab进行了数值仿真,得到了两种系统的同步误差曲线图、二维相图和三维相图,从而验证了混沌同步的准确性。Based on Ritz-Galerkin Method,the dynamic governing equations of a composite beam with clamped-fixed boundary conditions were simplified into the typical Duffing equations considering geometric nonlinear.A Duffing-Van Der Pol System was introduced.Parameter values of two systems reaching chaotic state commonly were presented according to their bifurcation diagrams.The accurate synchronization between Duffing system and DVP System （short for Duffing-Van Der Pol）was realized using the generalized projective synchronization method and their synchronization＇s controller was also acquired.Finally,numerical simulations for chaotic synchronization of the two systems were conducted with Matlab and synchronous error curve diagrams,2D-phase-trajectory diagrams,3D-phase-trajectory diagrams of the two systems were obtained.These diagrams were used to verify the correctness of chaotic synchronization.

关 键 词：复合材料 混沌同步 DVP系统 广义投影同步 

分 类 号：TB33[一般工业技术—材料科学与工程] O322[理学—一般力学与力学基础]