壁板边界松驰下颤振非线性动力特性分析

摘要

采用分离变量法和伽辽金法建立三维壁板的非线性气动弹性运动方程，用一阶活塞理论模拟壁板所受的气动力，分析了壁板的颤振边界及稳定性，进而取边界松弛因子，动压和面内力为分叉参数，研究壁板颤振时的分叉及混沌等复杂动力学特性。计算结果表明：边界松弛下壁板颤振系统表现出丰富的动力学行为，其分叉特性很复杂。随着边界松弛因子的增大，静态稳定区域缩小，而屈曲和混沌区域增大，系统稳定性降低。%A nonlinear dynamic analysis for a panel's flutter with boundary condition relaxation was conducted here.The flutter differential equations of a three-dimensional panel were built by using separation of variables and Galerkin method.The first piston theory was employed to calculate the aerodynamic load on the panel.The flutter boundary and stability for the flat panel were analyzed.Then,taking temperature,dynamic pressure and in-plane load as bifurcation parameters,their bifurcations and chaos behaviors were studied.The results demonstrated that the rich dynamic behaviors of the panel with boundary condition relaxation and its complex dynamic characteristics with variation of bifurcation parameters are revealed;both the buckling region and chaotic region increase with increase in relaxation of boundary conditions and the stability of the system decreases.