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| A FINITE DIFFERENCE METHOD FOR SIMULATING TRANSVERSE VIBRATIONS OF AN AXIALLY MOVING VISCOELASTIC STRING | |
| 作者姓名： | 赵维加 陈立群 |
| 作者单位： | Department of Mathematics，Shanghai Institute of Applied Mathematics and Mechanics，Department of Mechanical and Engineering Qingdao University，Qingdao 266071，Shandong Province，P.R.China Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，P.R.China，Shanghai University，Shanghai 200072，P.R.China Department of Applied Mathematics，Shanghai University，Shanghai 200072，P.R.China，University of Toronto，Ontario，M5s3G8 Canada |
| 摘 要： | A finite difference method is presented to simulate transverse vibrations of an axially moving string.By discretizing the governing equation and the equation of stress- strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two explicit difference schemes can be calculated alternatively, which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors,O(Δt~2 Δx~2).It also shows quite good stability for small initial values.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results. |
| 关 键 词： | 有限差分法 轴向移动 横向振动 黏弹性的 交互迭代 动力学分析 |
| 收稿时间： | 2003-05-30 |
| 修稿时间： | 2005-09-06 |
A finite difference method for simulating transverse vibrations of an axially moving viscoelastic string |
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| Wei-jia Zhao,Li-qun Chen,W. Zu Jean.A FINITE DIFFERENCE METHOD FOR SIMULATING TRANSVERSE VIBRATIONS OF AN AXIALLY MOVING VISCOELASTIC STRING[J].Applied Mathematics and Mechanics(English Edition),2006,27(1):23-28. | |
| Authors: | Wei-jia Zhao Li-qun Chen W Zu Jean |
| Institution: | 1. Department of Mathematics, Qingdao University, Qingdao 266071, Shandong Province, P.R.China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R. China 2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P.R. China;Department of Applied Mathematics, Shanghai University, Shanghai 200072, P.R. China 3. Department of Mechanical and Engineering, University of Toronto, Ontario, M5s3G8 Canada |
| Abstract: | A finite difference method is presented to simulate transverse vibrations of an axially moving string. By discretizing the governing equation and the equation of stress-strain relation at different frictional knots, two linear sparse finite difference equation systems are obtained. The two explicit difference schemes can be calculated alternatively, which make the computation much more efficient. The numerical method makes the nonlinear model easier to deal with and of truncation errors, O(Δt 2+Δx 2). It also shows quite good stability for small initial values. Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm, and dynamic analysis of a viscoelastic string is given by using the numerical results. Project supported by the National Natural Science Foundation of China (No.10472060), the Natural Science Foundation of Shanghai Municipality (No.04ZR14058) and the Shanghai Leading Academic Discipline Project (No.Y0103) |
| Keywords: | axially moving strings transverse vibration viscoelastic finite difference alternating iterative dynamical analysis |
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