外激励作用下亚音速二维粘弹性壁板系统的混沌运动

Chaotic Motion of Two-Dimensional Viscoelastic Panel with External Excitation in Subsonic Flow

为了研究壁板在亚音速气流和外激扰联合作用下的非线性运动特性,基于Hamilton原理,建立了外激励作用下亚音速粘弹性壁板的非线性运动方程,并采用Galerkin方法将其离散为常微分方程组,研究了系统的平衡点及其稳定性.利用Melnikov方法得到了壁板出现混沌运动时系统参数所满足的临界条件,分析了外激励幅值、频率及气流来流速度之间的临界关系,并与系统混沌运动的数值模拟结果进行了对比.结果表明:当无量纲动压值超过64.42时,壁板系统平衡点的个数及其稳定性均会发生改变;使用Melnikov方法确定的混沌运动临界参数与数值模拟结果相符,该方法可用于判定混沌运动是否发生.

In order to study the nonlinear dynamics of a panel subjected to external excitation in subsonic flow, the nonlinear governing motion equations of a two-dimensional forced subsonic viscoelastic panel were established by Hamilton theory, and discretized to a series of ordinary differential equations using the Galerkin method. Then, the system equilibrium points and their stability were analyzed, and Melnikov＇s method was used to obtain the critical values of system parameters for chaos appearance. The critical relations between the external excitation amplitude, frequency, and flow velocity were discussed and compared with the results of chaotic motions by numerical simulation. The results show that the number of equilibrium points and their stability will change after the dimensionless dynamic pressure exceeds 64.42, and the critical parameters determined by Melnikov＇s method match up to those obtained by numerical simulation. Therefore, the proposed method can be used to judge whether the chaotic motion happens or not.