梁动力学问题重心有理插值配点法  

Barycentric rational interpolation collocation method for solving dynamic problems of Euler-Bernoulli beams

作　　者：王兆清[1] 马燕[1] 唐炳涛[1] 

机构地区：[1]山东建筑大学工程结构现代分析与设计研究所,济南250101

出　　处：《振动与冲击》2013年第22期41-46,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51005137);山东建筑大学研究生教育创新计划(YC1005)

摘　　要：提出数值求解梁动力学问题的高精度重心有理插值配点法。采用重心有理插值张量积形式近似梁在任意时刻及位置挠度,运用配点法获得梁动力学问题控制方程与初边值条件的离散代数方程组。利用微分矩阵与矩阵张量积运算记号,将离散后代数方程组写成简洁矩阵形式。通过置换法施加边界条件及初始条件求解代数方程组,获得梁动力学问题在计算节点处位移值。数值算例表明,重心有理插值配点法具有算式简单、计算节点适应性好、程序实施方便、计算精度高等优点。The barycentric rational interpolation collocation method （BRICM） for solving dynamic problems of Euler-Bernoulli beams with high accuracy was presented. The deflections of a beam at anytime and anywhere were approximated with a tensor product form of barycentric rational interpolation in time domain and spatial domain, respectively. The discrete algebraic equations for governing equations, initial conditions and boundary conditions of a beam dynamic problem were constructed using the collocation method. Using notations of differentiation matrix and tensor product of matrices, the system of algebraic equations was written as a simple matrix form. The beam deflections on computational nodes were obtained by solving the system of algebraic equations with the replacement method to apply initial and boundary conditions. The numerical examples demonstrated that BRICM has merits of simple computational formulation, good applicability of node type, easy to program and high precision.

关 键 词：EULER-BERNOULLI梁 动力学问题 重心有理插值 微分矩阵 重心有理插值配点法 

分 类 号：O411.3[理学—理论物理]