梁动力学问题重心有理插值配点法

王兆清;马 燕;唐炳涛

振动与冲击 ›› 2013, Vol. 32 ›› Issue (22) : 41-46.

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PDF(1088 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (22) : 41-46.
论文

梁动力学问题重心有理插值配点法

  • 王兆清,马 燕,唐炳涛

作者信息 +

Barycentric rational interpolation collocation method for solving dynamical problems of euler-bernoulli beam

  • WANG Zhao-qing, MA Yan, TANG Bing-tao

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文章历史 +

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。

Abstract

The Barycentric Rational Interpolation Collocation Method (BRICM) for solving dynamical problems of Euler-Bernoulli beam with high accuracy is presented. The deflections of beam at anytime and in anywhere are approximated by tensor product form of barycentric rational interpolation in temporal field and in spatial domain, respectively. The discreted algebraic equations of governing equation, initial conditions and boundary conditions for dynamical problem of beam are constructed using collocation method. Using notations of differentiation matrix and tensor product of matrices, the system of algebraic equations can be formed as a neat matrices formulation. The deflections of beam on computational nodes are obtained by solving system of algebraic equations with replacement method to apply initial and boundary conditions. The numerical examples demonstrated that BRICM has merits of simple computational formulation, good adaptive of nodes 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

Key words

Euler-Bernoulli beam / dynamical problem / barycentric rational interpolation / differentiation matrix / barycentric rational interpolation collocation method

引用本文

导出引用
王兆清;马 燕;唐炳涛. 梁动力学问题重心有理插值配点法 [J]. 振动与冲击, 2013, 32(22): 41-46
WANG Zhao-qing;MA Yan;TANG Bing-tao. Barycentric rational interpolation collocation method for solving dynamical problems of euler-bernoulli beam [J]. Journal of Vibration and Shock, 2013, 32(22): 41-46

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