横纵激励下几何非线性复合材料层合梁的混沌同步

本文基于里兹-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。

Chaotic synchronization of geometric nonlinear composite beam under horizontal-vertical excitation

Based on Ritz-Galerkin Method, the governing equations of composite beam with the clamped-fixed boundary conditions can be simplified to the typical formal of Duffing Equations when geometric nonlinear is taken  into consideration. The Duffing-Van Der Pol System is introduced, and parameter values of two systems reaching the chaotic state commonly are obtained according to their bifurcation diagrams. The accurate synchronization among the Duffing System and the DVP System (short for Duffing-Van Der Pol) can be achieved by generalized projective synchronization method and their controller is also acquired. Finally, numerical analysis of chaotic synchronization is accomplished by Matlab and synchronous error curve diagrams, 2D-phase-trajectory diagrams, 3D-phase-trajectory diagrams can be gotten, these diagrams are used to verify the accuracy of chaotic synchronization.