改进有限条法在平壳条振动特性研究中的应用  

Application of Improved Finite Strip Method in the Study of Dynamic Characteristics of Flat Shell Strip

作　　者：陈良杰 高芳清[1,2] 王明[1] CHEN Liangjie;GAO Fangqing;WANG Ming(School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China;Applied Mechanics and Structural Safety Key Laboratory 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：《四川轻化工大学学报（自然科学版）》2023年第1期48-54,共7页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11872319)。

摘　　要：针对平壳条结构的振动特性问题,通过分析有限单元法的特点和应用,将改进的傅里叶级数法与有限单元法结合实现了任意边界条件的模拟,解决了平壳条结构对其梁函数边界条件的依赖性,从而提出一种高效、准确的半解析半数值方法—改进有限条法。根据Hamilton能量变分原理,推导出有限条元的刚度矩阵和质量矩阵并进行了平壳条结构自振特性分析。通过上机编程完成数值计算,并与商业有限元软件计算得到的结果进行对比分析,验证了该方法的有效性和准确性。进一步分析了截断级数、边界弹簧刚度系数、尺寸参数对系统频率的影响规律。Aiming at the problem of the vibration characteristics of flat shell and strip structures,the improved Fourier series method and the finite element method are combined to simulate arbitrary boundary conditions by analyzing the characteristics and applications of the finite element method.The dependence of flat shell and strip structures on the boundary conditions of their beam functions is solved,and an efficient and accurate semi-analytical and semi-numerical method,the improved finite strip method,is proposed.Based on Hamilton variational principle of energy,the stiffness matrix and mass matrix of finite element are derived,and the natural vibration characteristics of flat shell and strip structure are analyzed.The results obtained by computer programming are compared with those obtained by commercial finite element software to verify the validity and accuracy of the method.The influence of truncation series,boundary spring stiffness coefficient and dimension parameters on system frequency are further analyzed.

关 键 词：改进有限条法 改进傅里叶级数 半解析元法 平壳条 振动特性 

分 类 号：O327[理学—一般力学与力学基础]