改进傅里叶级数法求解封口锥柱球组合壳的自由振动  

Modified Fourier series method to solve the free vibration of the coupled conical-cylindrical-spherical shell with closed ends

作　　者：张帅[1,3] 李天匀 朱翔[1,2,3] 陈旭 ZHANG Shuai;LI Tian-yun;ZHU Xiang;CHEN Xu(School of Naval Architecture and Ocean Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;Collaborative Innovation Center for Advanced Ship and Deep-sea Exploration,Shanghai 200240,China;Hubei Key Laboratory of Naval Architecture and Ocean Engineering Hydrodynamics,Wuhan 430074,China)

机构地区：[1]华中科技大学船舶与海洋工程学院,湖北武汉430074 [2]高新船舶与深海开发装备协同创新中心,上海200240 [3]船舶与海洋水动力湖北省重点实验室,湖北武汉430074

出　　处：《振动工程学报》2021年第3期601-609,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51839005,51879113,51579109);中央高校基本科研业务费资助项目(2019kfyX⁃MBZ048)。

摘　　要：提出了一种改进傅里叶级数的半解析方法分析封口锥柱球组合壳的自由振动特性。基于能量泛函,结合经典薄板理论和Love壳体理论,建立了组合结构的理论模型,研究了不同柱壳长度,不同锥球半角以及不同厚度端板下锥柱球组合壳的固有频率。该方法下的各子壳结构位移由标准的傅里叶级数和辅助收敛函数组成,既克服了传统傅里叶级数在子壳结构交接处的不连续性,又提高了计算的收敛精度和速度。研究表明:该方法收敛性较好,所得理论计算结果与有限元结果比较一致。通过分析固有频率,发现改变长度,半角,端板厚度均会对锥柱球组合壳的自由振动产生较明显的影响。A semi-analytical method-modified Fourier series is proposed to solve the free vibration of the coupled conical-cylindricalspherical shell with closed ends.Based on energy function,the classical thin plate theory and Love shell theory are combined to construct the theoretical model of the coupled conical-cylindrical-spherical shell.The natural frequencies of the coupled structure with different cylindrical shell lengths,different semi angles of conical and spherical shell and different thicknesses of end plates are studied.The displacement of each substructure of the coupled shell is composed of the standard Fourier series and the auxiliary convergence functions.The introduction of the auxiliary functions can not only remove all the potential discontinuities of traditional Fourier series at the connections,but also improve the convergence precision and speed of calculation.The research shows that the present method has good convergence,which the calculation results show a good agreement with the finite element method results.By analyzing the natural frequency,it is found that the changes of length,semi-angle and thickness of end plates have obvious influence on the free vibration of the conical-cylindrical-spherical shell.

关 键 词：结构振动 锥-柱-球组合壳 圆端板 Love壳体理论 傅里叶里兹法 

分 类 号：O327[理学—一般力学与力学基础] U661.44[理学—力学]