带有负刚度装置的超音速壁板稳定性分析  

Stability Analysis of Supersonic Plate with Negative Stiffness Mechanism

作　　者：杨石芪 李鹏[1] 杨翊仁[1] YANG Shiqi;LI Peng;YANG Yiren(School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《四川轻化工大学学报（自然科学版）》2020年第5期57-62,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11772273)。

摘　　要：将水平预压弹簧构成负刚度装置(NSM),应用Hamilton原理及一阶活塞气动力模型,建立了带有NSM对边简支二维薄板在超音速流作用下的控制方程。运用Galerkin离散方法把偏微分方程转化为常微分方程;利用Hopf分岔代数判据计算系统的临界流速和颤振频率,并与没有NSM的薄板进行比较;最后考察NSM在板不同位置处对临界流速和颤振频率的影响。结果表明,NSM会降低系统的颤振频率;NSM在板中间位置时,会提高系统的临界流速;靠近板两端时,会降低系统的临界流速。The negative stiffness mechanism(NSM)is composed of horizontal preloading spring.The governing equations of a simple supported two-dimensional thin plate with NSM under the action of supersonic airflow are established through Hamilton principle and first-order piston theory.The Galerkin discrete method is used to transform the partial differential equation into an ordinary differential equation,and the Hopf bifurcation algebraic criterion is utilized to achieve the critical flow velocity and flutter frequency of the system,compared with the thin plate without NSM,finally,the effects of different positions of NSM on critical flow velocity and flutter frequency are investigated.The results show that NSM can reduce the flutter frequency of the system,increase the critical flow velocity of the system when NSM is in the middle of the plate,and reduce the critical velocity of the system when NSM is near the two ends of the plate.

关 键 词：负刚度装置 临界流速 活塞理论 GALERKIN方法 

分 类 号：V215[航空宇航科学与技术—航空宇航推进理论与工程]