轴向移动局部浸液单向板的1:3内共振分析  

ANALYSIS OF 1:3 INTERNAL RESONANCES FOR UNILATERAL PLATES PARTIALLY IMMERSED IN FLUID AND MOVING IN AXIAL DIRECTION

作　　者：李红影[1,2] 郭星辉[1,2] 王延庆[1] 李健[1] 谢里阳[2] 陈波[1] 

机构地区：[1]东北大学理学院应用力学研究所,沈阳110004 [2]东北大学机械工程与自动化学院,沈阳110004

出　　处：《力学学报》2012年第3期643-647,共5页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：考虑单向板的轴向速度、轴向张力、流固耦合作用以及阻尼等因素,基于由von Karman薄板大挠度方程得到的轴向移动局部浸液单向板的非线性振动方程,研究了外激励作用下单向板在1:3内共振情况时的非线性振动特性.首先利用Galerkin法对非线性振动方程离散化,然后分别应用数值法和近似解析法对离散后模态方程组进行求解,获得了系统内共振情况下复杂的幅频特性曲线,并讨论了周期解的稳定性.最后研究了1:3内共振系统平均方程组的运动分岔现象.Based on the nonlinear vibration equation of a unilateral plate partially immersed in fluid and moved in the axial direction, which is derived from von Karman thin plate equation with large deflection, the 1 ： 3 internal resonances characteristics of the unilateral plate under an external excitation are studied. The speed and tension of the unilateral plate in the axial direction, fluid-structure interaction and damping are considered. Galerkin method is used to disperse the vibration equation. The nonlinear modal equations are solved by applying numerical and approximate analytical techniques, respectively, and complex frequency- response curves with internal resonance are obtained. The stability of periodical solutions is discussed. At last, the bifurcation phenomenon of the averaged equations with 1 ： 3 internal resonances is studied.

关 键 词：局部浸液单向板 非线性 轴向移动 1内共振 分岔 

分 类 号：O322[理学—一般力学与力学基础]