采用高斯展开法分析组合式开口矩形Mindlin板的弯曲自振特性  

Flexural vibration analysis of rectangular Mindlin plate with combined openings using Gaussian expansion method

作　　者：杨舟 冯青松[1] 邓杰 张凌 郭文杰 YANG Zhou;FENG Qing‑song;DENG Jie;ZHANG Ling;GUO Wen‑jie(State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,China;Key Laboratory of Ocean Acoustic and Sensing,Northwestern Polytechnical University,Xi’an 710129,China)

机构地区：[1]华东交通大学轨道交通基础设施性能监测与保障国家重点实验室,江西南昌330013 [2]西北工业大学海洋声学信息感知重点实验室,陕西西安710129

出　　处：《振动工程学报》2022年第5期1130-1137,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51878277,52068029,52178423);江西省学科学术和技术带头人培养计划(20194BCJ22008);江西省重点研发计划(20192BBE50008)。

摘　　要：基于Mindlin板理论,将高斯展开法引入到组合式开口矩形板弯曲振动问题研究中。选取高斯小波函数作为位移形函数,其本身的局域化特性能够准确捕捉到局部开口处的特征,提高计算效率;定义了高斯函数的伸缩因子和平移因子,通过伸缩和平移变换生成一系列用于拟合开口板位移场的基函数,增大伸缩因子取值使得形函数具有更高的分辨率,进而能更精确地模拟更高频的振动场;以能量法为基本框架,建立了开口板的拉格朗日能量泛函,并引入人工弹簧模型模拟各种边界条件,将边界条件以弹性势能的方式附加到开口板的能量泛函之中。通过与有限元软件的计算结果对比,验证了该方法的准确性与适用性。Gaussian expansion method is introduced into the study of flexural vibration of rectangular plates with combined open‐ings based on the Mindlin plate theory.The localization characteristic of the Gaussian wavelet function can accurately capture the characteristics of the local opening and improve the computational efficiency by selecting the Gaussian wavelet function as the dis‐placement shape function.The expansion factor and shift factor of the Gaussian function are defined,and the basis functions used to fit the displacement field of the plate with opening are generated by a series of expansion and shift transformations.The larger the expansion factor is,the higher the resolution of the shape function will be.It can accurately simulate higher-frequency vibration field.The Lagrangian energy functional of the plate with opening is established by taking the energy method as the basic frame‐work.The artificial spring model is introduced into simulate various boundary conditions,and the influence of boundary conditions on vibration of plates is transformed into the influence of increased elastic potential energy on stiffness matrix.The accuracy and ap‐plicability of the method is verified by comparing the results of the research example with that of the finite element software,which provides a reference for practical engineering problems.

关 键 词：弯曲振动 组合式开口矩形板 MINDLIN板理论 高斯展开法 能量法 

分 类 号：O327[理学—一般力学与力学基础] TB123[理学—力学]