| 脉冲激励振动问题的高精度数值分析 |
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| 引用本文： | 王兆清,李淑萍,唐炳涛,赵晓伟. 脉冲激励振动问题的高精度数值分析[J]. 机械工程学报, 2009, 45(1). DOI: 10.3901/JME.2009.01.288 |
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| 作者姓名： | 王兆清 李淑萍 唐炳涛 赵晓伟 |
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| 作者单位： | 1. 山东建筑大学工程力学研究所,济南,250101
2. 山东警察学院治安系,济南,250014 |
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| 基金项目： | 山东建筑大学科研基金 |
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| 摘 要： | 利用数值稳定性好、计算精度高的重心Lagrange插值近似未知函数,得到未知函数各阶导数的微分矩阵,提出高精度数值分析任意激励下振动问题的重心插值配点法.采用附加法施加初始条件,得到一个n+2个方程n个未知量的代数方程组.利用最小二乘法求解线性方程组,得到振动位移,进而利用微分矩阵直接求得振动的速度和加速度.对于脉冲激励等复杂激励下的振动问题,将前一个时间区域末的位移和速度作为下一个时间区域的初始条件,分段进行数值分析.数值算例表明重心插值配点法在分析脉冲激励下的振动问题,具有非常高的计算精度.
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| 关 键 词： | 脉冲激励 振动 重心插值 配点法 数值分析 |
High Precision Numerical Analysis of Vibration Problems under Pulse Excitation |
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| WANG Zhaoqing,LI Shuping,TANG Bingtao,ZHAO Xiaowei. High Precision Numerical Analysis of Vibration Problems under Pulse Excitation[J]. Chinese Journal of Mechanical Engineering, 2009, 45(1). DOI: 10.3901/JME.2009.01.288 |
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| Authors: | WANG Zhaoqing LI Shuping TANG Bingtao ZHAO Xiaowei |
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| Affiliation: | WANG Zhaoqing~1 LI Shuping~2 TANG Bingtao~1 ZHAO Xiaowei~1 1.Institute of Engineering Mechanics,Sh,ong Jianzhu University,Jinan 250101,2.Department of Public Security,Sh,ong Police College,Jinan 250014 |
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| Abstract: | The differential matrices of derivatives are constructed by using barycentric Lagrange interpolation which has good numerical stability and high computing precision.The barycentric interpolation collocation method for analyzing the vibration problems under arbitrary excitation is presented.The vibration differential equation and two initial conditions are transformed into a set of algebraic equation system and two algebraic equations respectively.Applying attached method to impose initial conditions,a new s... |
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| Keywords: | Pulse excitation Vibration Barycentric interpolation Collocation method Numerical analysis |
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