基于改进傅里叶级数的黏弹性夹层板动力问题的数值算法研究  

Numerical algorithm for dynamic problems of viscoelastic sandwich plates based on improved Fourier series

作　　者：马乾瑛[1] 梅杨 孙正 MA Qian-ying;MEI Yang;SUN Zheng(Department of Architecture and Civil Engineering,Chang’an University,Xi’an 710061,China)

机构地区：[1]长安大学建筑工程学院,西安710061

出　　处：《计算力学学报》2024年第5期894-902,共9页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51208041);陕西省自然科学基金(2020SF-382,2014JM2-5080);长安大学教学改革研究项目(20211822,300103292815)资助。

摘　　要：本文提出了一种基于改进傅里叶级数的新型数值算法,用于求解任意边界条件下黏弹性夹层板的自由振动特性。该算法利用一阶剪切理论建立面外位移场,采用改进的傅里叶级数拟合位移容许函数,结合Rayleigh-Ritz法计算动能和势能,并利用Hamilton变分原理得到振动特征矩阵方程。计算结果表明,无论是梁式板结构还是各种边界条件下的夹层板结构,该算法得到的自振频率和损耗因子与解析解、2D有限元解、数值计算法和ABAQUS有限元软件等计算结果相比,误差均不超过1%,计算效率提高了10倍,并且克服了传统方法只能求解特定边界下振动问题的局限性。本文建立的方法具有收敛性好、计算效率高和适应性强等特点。In this paper,a new numerical algorithm based on improved Fourier series is proposed to determine the free vibration characteristics of viscoelastic sandwich plates under arbitrary boundary conditions.The algorithm uses the first-order shear theory to establish the out-of-plane displacement field and the improved Fourier series to fit the displacement tolerance function,combines the Rayleigh-Ritz method to calculate the kinetic energy and potential energy,and uses the Hamilton variational principle to obtain the characteristic matrix equation.The results show that the errors of the natural frequencies and loss factors obtained by the algorithm are not more than 1% compared with the analytical solution,2D finite element solution,numerical calculation method and ABAQUS finite element software,whether it is a beam-plate structure or a sandwich plate structure under various boundary conditions.The calculation efficiency is increased by 10 times,and the limitation that the traditional method can only solve the vibration problem under specific boundary conditions is overcome.The method established in this paper has the characteristics of fast convergence,high calculation efficiency and strong adaptability.

关 键 词：黏弹性夹层板 任意边界条件 改进的傅里叶级数 自由振动 

分 类 号：O327[理学—一般力学与力学基础]