移位Bernstein多项式算法对粘弹性梁的数值分析  

Numerical analysis of viscoelastic beam by the shifted Bernstein polynomial algorithm

作　　者：金素花 解加全 韩存弟 孙虹霞[1] 陈一鸣[1] JIN Su-hua;XIE Jia-quan;HAN Cun-di;SUN Hong-xia;CHEN Yi-ming(School of Science,Yanshan University,Qinhuangdao 066004,Hebei,China;Department of Mathematics,Taiyuan Normal University,Jinzhong 030619,Shanxi,China;Institute of Advanced Forming and Intelligent Equipment,Taiyuan University of Technology,Taiyuan 030024,Shanxi,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004 [2]太原师范学院数学系,山西晋中030619 [3]太原理工大学先进成形与智能装备研究院,山西太原030024

出　　处：《西北师范大学学报（自然科学版）》2022年第3期31-36,共6页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(52005360);山西省高等学校科技创新项目(2021L403)。

摘　　要：提出了一种新的求解变分数阶粘弹性梁本构方程的数值算法.将移位Bernstein多项式作为基函数逼近梁的位移函数,推导出整数阶和变分数阶微分算子矩阵;将粘弹性梁的位移控制方程转化成矩阵乘积的形式,并采用配点法将矩阵方程重新转化成代数方程组,在时域内直接获得位移控制方程的数值解.数值算例精确解与数值解的比较结果验证了算法的高效性;通过分析粘弹性梁在不同载荷下的位移数值解,进一步验证了算法的实用性.This paper proposes a new numerical algorithm for solving the constitutive equation of variable fractional order viscoelastic beams.The shifted Bernstein polynomial is used as the basis function to approximate the displacement function of the beam and the matrices of integer order and variable fractional order differential operators are derived.At the same time,the displacement governing equation of the viscoelastic beam is transformed into the form of matrix product.The matrix equation is re-transformed into algebraic equations by the configuration method,and the numerical solution of the displacement governing equation can be directly obtained in the time domain.The comparison between the exact solution and the numerical solution of the numerical example proves the efficiency of the algorithm proposed in this paper.In addition,the practicability of the algorithm is further verified by analyzing the displacement numerical solutions of the viscoelastic beam under different loads.

关 键 词：变分数阶粘弹性梁 移位Bernstein多项式 算子矩阵 数值解 

分 类 号：O241.8[理学—计算数学]