中文核心期刊
CSCD来源期刊
中国科技核心期刊
RCCSE中国核心学术期刊
重庆交通大学学报（自然科学版）

重庆交通大学学报（自然科学版） ›› 2012, Vol. 31 ›› Issue (1): 6-10.DOI: 10.3969/j.issn.1674-0696.2012.01.02

• • 上一篇    下一篇

梁自由横振动方程的有限差分方法

杜 绍 洪   

  1. 重庆交通大学 理学院，重庆 400074
  • 收稿日期:2011-06-13 修回日期:2011-07-30 出版日期:2012-02-15 发布日期:2015-04-15
  • 作者简介:杜绍洪 (1972-)，男，四川阆中人，讲师，博士，主要从事有限元和偏微分方程数值解方面的研究。E-mail:dushhong@gmail.com。
  • 基金资助:
    重庆市自然科学基金项目(CSTC, 2010BB8270)

Finite Difference Method of Free Transverse Vibration Equations of Beams

Du Shaohong   

  1. School of Science, Chongqing Jiaotong University, Chongqing 400074, China
  • Received:2011-06-13 Revised:2011-07-30 Online:2012-02-15 Published:2015-04-15

PDF

摘要： 以简支梁的自由横振动问题为背景，求解一个非稳态四阶线性偏微分方程的初边值问题。通过引进辅助函数组，将四阶问题转化为二阶混合初边值问题。对两个辅助函数和二阶混合初边值问题进行离散并消掉中间变量，对由简支梁两端挠度为零得来的二阶偏微分边界条件进行近似处理，构造出求解四阶非稳态线性偏微分方程的差分隐格式。数值实验表明构造的隐格式绝对稳定并且具有很高的精度阶。

关键词: 梁横振动方程, 有限差分方法, 差分格式的绝对稳定

Abstract: A fourth order partial differential equation which originates from the free transverse vibration of beams, was changed into a second order mixed initial boundary value problem by introducing a couple of auxiliary functions. An implicit scheme of difference was constructed by discretization of two auxiliary functions and the second order mixed initial boundary value problem in which intermediate variables were eliminated and the second order boundary value conditions derived from vanishing deflection at both ends of the beam were approximated. Numerical experiments showed that the developed implicit scheme was absolutely stable and guaranteed a very high accuracy.

Key words: vibration equation of beams, finite difference method, absolutely stable difference scheme

中图分类号: