基于里兹法的圆柱壳振动特性分析  

Vibration characteristics analysis of cylindrical shell based on Ritz method

作　　者：庞福振[1] 高聪 李玉慧 秦宇璇 PANG Fuzhen;GAO Cong;LI Yuhui;QIN Yuxuan(College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,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

出　　处：《华中科技大学学报（自然科学版）》2020年第7期71-76,共6页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51209052,51679053,51709063);哈尔滨工程大学博士研究生科研创新基金资助项目(HEUGIP201902);国家重点研发计划资助项目(2016YFC0303406);山东省重点研发计划资助项目(2019JZZY010125);总装预研基金资助项目(6140210020105);海军预研项目;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)。

摘　　要：基于一阶剪切变形理论构建分析模型,引入耦合弹簧技术模拟圆柱壳结构不同边界条件;位移函数采用改进的傅里叶级数以消除边界条件的不连续性,并基于里兹法求得出中厚功能梯度圆柱壳固有频率,在收敛性分析的基础上,研究不同边界条件、结构参数和材料参数对中厚功能梯度圆柱壳自由振动特性的影响,并将计算结果与文献、试验和有限元结果进行对比,验证本文方法的可行性.研究结果表明:同一模态参数下,功能梯度圆柱壳含有自由边界的频率参数较其他边界小;圆柱壳结构厚度对频率参数影响较大;剪切修正因子及幂指数对结构频率参数影响较小.The analytical model was built based on the first-order shear deformation theory,and the different boundary conditions of the cylindrical shell were simulated by the coupling spring technique.The improved Fourier series were applied to displacement admissible functions to eliminate the discontinuity of boundary conditions,and the natural frequency of medium thick functionally graded cylindrical shells were obtained by Ritz method.In addition,the results were compared with those of the existing literatures,experiment and finite element method to verify the feasibility.Research results show that the frequency parameters of the functionally graded cylindrical shell with free boundary are smaller than those of other boundaries under the same modal parameters.The thickness of cylindrical shell has a great influence on the frequency parameters,and the shear correction factor and power exponent have little influences on the structure frequency parameters.

关 键 词：半解析法 功能梯度圆柱壳 一般边界条件 自由振动 里兹法 

分 类 号：TB52[理学—物理]