复合材料矩形悬臂板的稳定性和分岔分析  

Stability and Bifurcation Analysis of a Composite Laminated Cantilever Rectangular Plate

作　　者：安凤仙[1] 杨立波[1] AN Feng-xian;YANG Li-bo(Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai'an Jiangsu 223001, China)

机构地区：[1]淮阴工学院数理学院,江苏淮安223001

出　　处：《淮阴工学院学报》2021年第5期15-23,共9页Journal of Huaiyin Institute of Technology

基　　金：国家自然科学基金(11772148);江苏省产学研合作项目(BY2020228)。

摘　　要：利用理论分析和数值模拟两种方法研究了面内激励下超音速气流中复合材料矩形悬臂板的稳定性和分岔行为。考虑3种类型退化平衡点的情况,分别为非共振情形下1对纯虚特征根、1个零特征根和1对纯虚特征根以及2对纯虚特征根。利用规范型理论,得到了系统发生静态分岔、Hopf分岔和2-D圆环面分岔的转迁曲线。此外,利用四阶Runge-Kutta算法验证了理论分析结果的正确性。理论分析结果对于优化工程结构的参数设计具有重要意义。Stability and bifurcation behaviors of a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations are investigated by using both analytical and numerical approaches.Three types of degenerated equilibrium points are considered,which are characterized by a pair of pure imaginary eigenvalues,a simple zero and a pair of pure imaginary eigenvalues,and two pairs of pure imaginary eigenvalues in non-resonant case.With the aid of normal form theory,the transition curves leading to static bifurcation,Hopf bifurcation and 2-D torus bifurcation are obtained.Moreover,numerical simulations obtained by employing the fourth-order Runge-Kutta method agree with the analytical predictions.The analytical results obtained here can help us to optimize the design of the structural parameters of related engineering structures.

关 键 词：矩形悬臂板 稳定性 分岔 规范型 

分 类 号：O322[理学—一般力学与力学基础]