一类含符号函数的无穷积分的高效数值解法  

Efficient numerical solutions for a class of infiniteintegrals with signed functions

作　　者：葛新广 卢嘉康 张梨荣 罗臻[2] GE Xinguang;LU Jiakang;ZHANG Lirong;LUO Zhen(School of Civil and Architecture Engineering,Liuzhou Institute of Technology,Liuzhou 545616,China;School of Civil and Architecture Engineering,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]柳州工学院土木建筑工程学院,广西柳州545616 [2]广西科技大学土木建筑工程学院,广西柳州545006

出　　处：《广西科技大学学报》2024年第3期48-55,共8页Journal of Guangxi University of Science and Technology

基　　金：国家自然科学基金项目(51368005);柳州工学院高层次人才项目(202201)资助。

摘　　要：基于频域法研究几类随机激励下工程结构的动力响应,需要求解4种含符号函数在无穷区间的积分解,而该4种积分式目前存在计算效率和精度的问题。首先,根据积分运算法则将4种积分式的计算转换为一种积分式的计算;其次,基于留数定理和高斯-雅克比积分提出了4种积分式的高效简明数值解法;最后,通过算例研究了传统方法受积分上限和积分区间的影响、本文方法受高斯-雅克比积分节点数的影响。结果表明:传统方法的计算结果受积分区间和积分上限的影响较大,而本文方法取25个高斯-雅克比积分节点数即可获得较高的精度,且具有较高的计算效率。To study the dynamic response of engineering structures under some random excitation based on frequency domain method,it is necessary to solve four infinite integrals with signed functions for which,however,there is computational efficiency and accuracy problem.Firstly,the calculation of four integral equations was converted into that of one integral equation according to the integral arithmetic.Secondly,an efficient and concise numerical solution for the above integral equations was presented based on the residue theorem and Gaussian-Jacobian integration.Finally,through numerical examples,the effect of the integration upper limit and integration interval on the traditional method and that of the number of Gaussian-Jacobian integration nodes on the method in this paper were studied.The results show that the calculation results of the traditional method are greatly affected by the integration interval and integration upper limit.However,the method in this paper can achieve high accuracy and computational efficiency by taking 25 Gaussian-Jacobian integration nodes.

关 键 词：无穷积分 符号函数 高斯-雅克比积分 高效数值解 

分 类 号：TU311.3[建筑科学—结构工程]