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基于Kelvin粘弹模型,根据Von Karman大变形应变-位移关系和一阶活塞气动力理论,运用伽辽金方法建立了三维粘弹壁板颤振方程,并采用Rouge-Kutta法进行数值积分,分析粘弹阻尼,面内压力及壁板几何尺寸对粘弹壁板颤振的影响,进而取动压为分叉参数,研究粘弹壁板颤振时的分叉及混沌等特性。结果表明:随着粘弹性阻尼的增大,系统的静态稳定区域先减小后增大,而静态屈曲解儿乎不受影响,同时发现混沌运动区域随着粘弹阻尼的增大而快速减小。当取动压为分叉参数时发现粘弹壁板分叉特性很复杂,系统由屈曲状态进入混沌振动,再经历一系列的分叉进入简谐极限环振动状态;而较大面内压力和较小的长宽比不利于粘弹壁板的稳定。
Based on the Kelvin viscoelastic model and the Von Karman large strain-displacement relationship and the first-order piston aerodynamic theory, a three-dimensional viscoelastic panel flutter equation is established by using the Galerkin method. The Rouge-Kutta method is used for numerical integration and analysis Viscoelastic damping, in-plane pressure and wall geometry on the flutter of the viscoelastic panel are investigated. Then the bifurcation parameters are taken as the moving pressure, and the bifurcation and chaos in viscoelastic panel flutter are studied. The results show that with the increase of viscoelastic damping, the static stability of the system first decreases and then increases, while the static buckling solution is almost unaffected. At the same time, it is found that the area of chaotic motion decreases rapidly with the increase of viscoelastic damping small. When the bifurcation parameters are taken as the bifurcation parameters, the bifurcation characteristics of the viscoelastic panel are complex. The system enters the chaotic vibration from the buckling state and then undergoes a series of bifurcations into the vibrational state of the harmonic limit cycle. The larger in-plane pressure and Smaller aspect ratio is not conducive to the stability of viscoelastic panels.