基于一阶剪切变形理论的功能梯度球环振动特性  

Free vibration characteristics of functionally graded spherical torus based on first-order shear deformation theory

作　　者：高晟耀 彭德炜 唐宇航 高聪 李玉慧 谷瑞钊 GAO Shengyao;PENG Dewei;TANG Yuhang;GAO Cong;LI Yuhui;GU Ruizhao(Naval Research Academy,Beijing 100161,China;College of Shipbuilding Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]中国人民解放军92578部队,北京100161 [2]哈尔滨工程大学船舶工程学院,哈尔滨150001

出　　处：《复合材料学报》2020年第4期935-943,共9页Acta Materiae Compositae Sinica

基　　金：国家重点研发计划(2016YFC0303406);总装预研基金(6140210020105);国家自然科学基金(51209052,51709063);中央高校基本科研业务费资助项目(HEUCFD1515,HEUCFM170113);十三五预研基金;中国博士后基金(2014M552661)。

摘　　要：提出一种半解析法分析了一般边界条件下中等厚度功能梯度球环结构的自由振动特性。基于一阶剪切变形理论推导了中等厚度功能梯度球环结构公式,其中位移函数用改进傅里叶级数表示以消除边界的不连续性,并利用弹簧参数法来模拟一般边界条件;利用里兹法求解得到功能梯度球环结构的固有频率;在收敛性分析的基础上,将本文结果与有限元法、试验数据和文献数据进行了对比,并探讨相关参数的影响。研究表明,本文提出的方法收敛性好,求解精度高;功能梯度球环结构频率参数随厚度和剪切修正系数的增大而增大。A semi-analytical method to investigate the free vibration characteristics of moderately thick functionally graded material(FGM)spherical torus structures with general boundary conditions was proposed. The theoretical formulas were derived by applying the first-order shear deformation theory, in which the displacement admissible functions were expressed by Improved Fourier Series to eliminate the discontinuity of the boundary. The general boundary conditions of the functionally graded spherical torus structure were simulated by different spring parameters. The natural frequencies of functionally graded spherical torus were obtained by Ritz method. The data in this paper were compared with those obtained by finite element method, experiment and literatures based on convergence analysis, and the influences of correlation parameter were studied. The results show that the proposed method has advantages of good convergence and high accuracy. The frequency parameter of functionally graded spherical torus structures increases with the increase of thickness and shear correction factors.

关 键 词：一阶剪切变形理论 功能梯度材料 球环 一般边界条件 自由振动 

分 类 号：TB123[理学—工程力学] TB52[理学—力学]