大展弦比板弯扭耦合受迫振动分析  

Analysis of Flexural Coupled Forced Vibration of High-Aspect Ratio Plate

作　　者：王卓[1] 毛晓晔 丁虎[1] 陈立群[1] Wang Zhuo;Mao Xiaoye;Ding Hu;Chen Liqun(School of Mechanics and Engineering Science,Shanghai Frontier Science Center of Mechanoinformatics,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学力学与工程科学学院上海力学信息学前沿科学中心,上海200444

出　　处：《动力学与控制学报》2024年第1期27-36,共10页Journal of Dynamics and Control

基　　金：国家自然科学基金青年基金项目(12002195);国家自然科学基金杰出青年基金(12025204);上海市教育委员会科研创新计划项目(2019-01-07-00-09-E00018);上海市科学技术委员会浦江人才计划(A类)(20PJ1404000)。

摘　　要：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.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.

关 键 词：大展弦比板 弯扭耦合振动 受迫振动 谐波平衡法 

分 类 号：O322[理学—一般力学与力学基础]