改进有限条法用于矩形薄板的振动分析  

Improved Finite Strip Method for Vibration Analysis of Rectangular Thin Plates

作　　者：王明[1] 高芳清[1,2] 陈良杰 WANG Ming;GAO Fangqing;CHEN Liangjie(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China;Key Laboratory of Applied Mechanics and Structural Safety of Sichuan Province,Southwest Jiaotong University,Chengdu 611756,China)

机构地区：[1]西南交通大学力学与航空航天学院,成都611756 [2]西南交通大学应用力学与结构安全四川省重点实验室,成都611756

出　　处：《噪声与振动控制》2023年第3期66-70,82,共6页Noise and Vibration Control

基　　金：工信部基金资助项目(MJZ-2018-S-51)。

摘　　要：工程应用中的薄板可视为由条状薄板组成的结构,如矩形薄板、蜂窝薄板结构等。各类解析法精度较好但应用不够灵活,有限单元法在计算较为灵活但过大的矩阵致使求解效率低下。结合有限元法和解析法的优点,建立矩形形状的有限板条。采用一维离散、一维解析的半解析函数构造薄板的位移函数,其中离散方向采用Hermite插值构造来满足薄板的位移连续和转角连续,解析方向通过改进的傅里叶级数描述相应边界的梁函数。以矩形薄板的振动为研究内容,通过将得到的薄板固有频率与有限元软件计算结果进行对比,验证了基于有限条法所建立的计算模型的有效性,分析边界弹簧刚度和傅里叶级数截断值对计算结果收敛性的影响。The thin plate in engineering application can be regarded as a structure composed of strips of thin plates,such as rectangular thin plate,honeycomb thin plate and so on.Various analytical methods are of better accuracy but not flexible,while finite element method(FEM)is pertinent in calculation but inefficient.Combining the advantages of the FEM and the analytical method,the finite rectangular slats model is established.In this method,the semi-analytical function combining one-dimensional discrete and one-dimensional analytical functions is applied to construct the displacement function of the finite slats.In the discrete direction,the Hermite interpolation is used to construct the displacement function,which can satisfy the displacement continuity and rotation angle continuity conditions;and in the analytical direction,the improved Fourier series is employed to describe the beam functions of the corresponding boundaries of the strip.With a rectangular thin plate as the example,its natural frequencies of vibration are calculated with this method,and the results are compared with those obtained by means of FEM software.The correctness and efficiency of the finite strip method are verified.Finally,the influence of the spring support stiffness of the boundary and the truncation of the Fourier series on the convergence of the computation output is analyzed.

关 键 词：振动与波 有限条法 改进傅里叶级数 矩形薄板 振动特性 

分 类 号：O327[理学—一般力学与力学基础]