亚音速气流下不对称双跨黏弹性板的非线性振动特性研究

Nonlinear Vibration of Asymmetrical Two-span Viscoelastic Plates in Subsonic Airflow

研究了亚音速气流作用下不对称双跨黏弹性板的非线性振动特性。考虑von Kármán几何大变形,利用Hamilton原理,建立了不对称双跨黏弹性板的非线性运动方程,并对其采用分离变量法进行了离散。运用线性势理论得到了亚音速气流的气动压力表达式。利用板的边界条件和中间支承条件得到了双跨板的模态函数。研究了来流速度对双跨板非线性振动特性的影响,分析了不对称程度和黏弹性阻尼系数对结构发生混沌运动的影响。

The nonlinear vibration properties of asymmetrical two-span viscoelastic plates in subsonic airflow is investigated. Considering the von Karman, large deformation theory, the partial differential equation of motion of the structural system is established using the Hamilton’s principle, and it is discretized by the method of variable separation. The subsonic aerodynamic pressure induced by the transverse motion of the structure is obtained from the linear potential flow theory. The mode shapes of the two-span plate are obtained by using the boundary and in-ternal support conditions. The effect of the airflow velocity on the nonlinear vibration characteristics of the two-span plate is studied by numerical simulations. And the influences of the asymmetry degree and viscoelastic damping co-efficient on the chaotic motion of the structure are analyzed.