大展弦比板弯扭耦合受迫振动分析

对于工程广泛存在的大展弦比结构,首次研究了大展弦比板弯扭耦合受迫振动响应.考虑弦向相对弯曲刚度远大于展向弯曲刚度,将弦向截面等效为刚体,考虑其绕展向轴线的扭转,应用Hamilton原理分别计算大展弦比板的势能与动能,建立两端简支的大展弦比板弯扭耦合受迫振动的动力学控制方程.将动力学控制方程进行Galerkin截断后,通过谐波平衡法和微分求积法/微分求积单元法,计算得到了大展弦比模型弯扭耦合受迫振动稳态响应的解析解及数值解,同时验证了解的截断收敛性及谐波收敛性.最后研究了外激励幅值对结构受迫振动响应的影响.结果将为工程中广泛存在的大展弦比结构设计提供指导.

Analysis of Flexural Coupled Forced Vibration of High Aspect Ratio Plate

For extensively existed high-aspect ratio structures in engineering, the bending-torsional-coupled vibration of the high-aspect ratio plate is studied for the first time. As the relative stiffness along the chordwise direction is far bigger than that of the spanwise, the chordwise section is simplified as a rigid body, while that in the spanwise direction is flexible. The Hamilton’s principle is applied to establish the governing equation of the bending-torsional-coupled vibration of the high-aspect ratio plate with simple supports at both ends. After projecting the governing equation into modal space via Galerkin method, the analytical results and numerical solutions of the bending-torsional-coupled vibration are obtained by the harmonic balance method and DQEM/DQM respectively. The convergence of the modal projection and the harmonic expansion are also verified. Finally, the influence of the external excitation on the forced vibration is studied. The results provide guidance for the design of high-aspect ratio structures in engineering.