双曲率组合结构自由振动特性分析  

Free vibration analysis of joined doubly-curved shells of revolution

作　　者：庞福振[1,2] 李海超 彭德炜[1] 霍瑞东 缪旭弘 PANG Fu-zhen;LI Hai-chao;PENG De-wei;HUO Rui-dong;MIAO Xu-hong(College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China;Yantai Research Institute and Graduate School,Harbin Engineering University,Yantai 264000,China;Naval Research Academy,Beijing 100161,China)

机构地区：[1]哈尔滨工程大学船舶工程学院,黑龙江哈尔滨150001 [2]哈尔滨工程大学烟台研究院,山东烟台264000 [3]中国人民解放军92578部队,北京100161

出　　处：《振动工程学报》2020年第3期441-449,共9页Journal of Vibration Engineering

基　　金：国家重点研发计划课题(2016YFC0303406);总装预研基金资助项目(6140210020105);国家自然科学基金资助项目(51209052,51679053);山东省重点研发计划课题(2019JZZY010125);中央高校基本科研业务费资助项目(HEUCFD1515,HEUCFM170113);中国博士后基金资助项目(2014M552661);哈尔滨工程大学博士研究生科研创新基金资助项目(HEUGIP201801)。

摘　　要：针对双曲率组合结构自由振动特性分析方法有待完善等问题,基于半解析法开展了双曲率组合壳结构自由振动特性研究。基于Flügge薄壳理论,首先将抛物壳-圆柱壳-球壳组合结构在交界面处进行分解,获得抛物壳、圆柱壳和球壳子结构;再将抛物壳、圆柱壳和球壳子结构沿周向进一步分解为若干壳段,用沿径向的Jacobi多项式和周向的Fourier级数来表示各个壳段的位移函数,并用不同的弹簧刚度对组合结构的边界条件和壳体内的连续性条件进行模拟;最后,基于Rayleigh-Ritz法获得双曲率组合结构的振动模态,探索复杂边界条件下双曲率组合结构自由振动特性。在此基础上,将双曲率组合结构自由振动频率与已有文献及有限元法计算结果进行对比分析,验证了方法的收敛性和有效性,研究成果可为复杂边界条件双曲率组合结构自由振动特性分析提供方法依据和数据积累。Aiming at the problem that the analysis method of free vibration characteristics of double-curvature composite structures needs to be improved,the free vibration characteristics of double-curvature composite shell structures are investigated based on a semi-analytical method.Based on Flügge’s thin shell theory,the double-curvature composite shell structures are firstly divided into substructures of paraboloidal,cylindrical and spherical shells at the interface.Secondly,the paraboloidal,spherical and cylindrical shells are further divided into several shell segments along the radial direction,the displacement functions of each shell segment are represented by Jacobi polynomials along the axis direction and the Fourier series along the radial direction,and the continuous conditions at the interface and the boundary conditions at the two ends of the composite shells are modeled using different spring stiffness.Finally,the free vibration frequencies of double-curvature composite shell are obtained based on Rayleigh-Ritz method.To test the convergence,validity and accuracy of present method,numerical results are compared with those obtained using the FEM and existing literatures,and very good agreement is observed.The results of this paper can provide a judging method and reference data for free vibration characteristics of double-curvature composite shell with complex boundary conditions.

关 键 词：结构振动 自由振动 半解析法 双曲率组合结构 复杂边界条件 

分 类 号：O327[理学—一般力学与力学基础] TB123[理学—力学]