华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (5): 69-75,92.

• 应用数学 • 上一篇    下一篇

电磁发射轨道受余弦函数磁压力作用的瞬态响应

刘 峰, 刘 文   

  1. 燕山大学~~理学院, 河北~~秦皇岛市 066004
  • 收稿日期:2011-12-01 修回日期:2012-03-01 出版日期:2012-09-25 发布日期:2012-09-29

Transient influence on the electromagnetic launch rail under a cosine function of the magnetic pressure

LIU Feng, LIU Wen   

  1. College of Science, Yanshan University, Qinhuangdao Hebei 066004, China
  • Received:2011-12-01 Revised:2012-03-01 Online:2012-09-25 Published:2012-09-29

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摘要： 研究影响电磁轨道发射的摩擦阻尼力因素. 将电磁发射装置的轨道模拟为移动载荷作用下的弹性基础梁, 采用欧拉梁理论建立梁的力学模型,
利用积分变换及其逆变换等方法推导出简谐压力作用下轨道的瞬态响应解析解; 通过\,MATLAB\,数值算例分析得到: 弹性系数、粘滞外阻尼系数和摩擦阻尼系数对梁瞬态动力响应产生不同程度的影响. 这为今后求解更高阶偏微分方程的初值问题及其改进电磁发射装置的性能提供了理论依据.

关键词: 电磁发射轨道, 力学模型, 傅里叶变换, 拉普拉斯变换, 逆变换, 瞬态响应

Abstract: This paper studied the friction damping factors that influence electromagnetic rail launching. An electrical magnetric launcher orbit was simulated into an elastic foundation beam under a movement loading, a mathematical model of beam was established by using Euler beam theory, and the analytic solution of the flexural deflections of an orbit involving exponential functions of the dynamics problem under a simple harmonic pressure was derived with the help of the integral transformation, the inverse transformation and so on. The results of the numerical examples with MATLAB
software showed that the elasticity coefficient, the viscous external damping coefficient and the coulomb damping coefficient have different influences on the transient dynamic response. So it provides sufficient theory evidence about the initial value problem of solving a higher order partial differential equation and improving the performance of an electromagnetic emission device.

Key words: electromagnetic launch rail, mechanical model, Fourier transformation, Laplace transformation, inverse transformation, transient response

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