矩形薄板的混沌运动研究  

Chaotic Motion of a Rectangular Thin Plate

作　　者：孟令常[1] 武洪跃 祝丹梅[1] 范传强[1] 玉姣 

机构地区：[1]辽宁石油化工大学理学院,抚顺113001

出　　处：《科学技术与工程》2015年第28期1-3,9,共4页Science Technology and Engineering

基　　金：国家自然科学基金;青年科学基金项目(11304137)资助

摘　　要：研究了气流和面外激励共同作用下四边完全简支的矩形薄板的混沌运动行为。考虑几何大变形理论,利用Hamilton变分原理,建立了气流作用下矩形薄板的非线性振动偏微分方程;并将偏微分方程离散为常微分方程。运用线性势理论,得到了气流的气动力。用梅尔尼科夫方法得到了混沌运动存在的必要条件;数值模拟给出了振动系统的分叉图、相图和庞加莱截面,验证了必要条件的正确性。研究结果表明,随着来流速度的增加,矩形薄板会发生不稳定振动,出现混沌运动。The chaotic motion of a fully simply supported rectangular thin plate subjected to axial subsonic airflow and transverse harmonic excitation is analyzed. Considering on the large deformation theory,the partial differential equation of motion of the structural system is formulated using the Hamilton＇s principle and transformed into a set of ordinary differential equations through the Galerkin＇s method. The aerodynamic pressure induced by the transverse motion of the plate is derived from the linear potential flow theory. For the structural system,the Melnikov＇s method is adopted to give an analytical expression of the necessary condition for the chaotic motion of the plate. Numerical simulations are carried out to obtain the bifurcation diagrams,phase portraits and Poincare maps to verify the validity of the analytical results. The results show that when the flow velocity increases,the plate will be unstable,and the chaotic motion of the plate will happen.

关 键 词：矩形薄板 混沌运动 几何大变形 梅尔尼科夫方法 

分 类 号：O322[理学—一般力学与力学基础]