大学物理 ›› 2019, Vol. 38 ›› Issue (6): 45-.doi: 10.16854 /j.cnki.1000-0712.180577

• 大学生园地 • 上一篇    下一篇

共振频率激励下弦振动定解问题的求解

何家奇,韩社教   

  1. 1. 西安电子科技大学空间科学与技术学院,陕西西安710126; 2. 西安电子科技大学物理与光电工程学院,陕西西安710071; 3. 株洲瑞尔泰机电科技有限公司,湖南株洲412007
  • 收稿日期:2018-10-18 修回日期:2018-12-26 出版日期:2019-06-20 发布日期:2019-07-02
  • 通讯作者: 韩社教,E-mail: wanghy@ xjtu.edu.cn
  • 作者简介:何家奇( 1998 —) ,男,四川南充人,西安电子科技大学空间科学与技术学院2015 级本科生.

Solution of string vibrating problem under the resonant frequency incentive

HE Jia-qi,HAN She-jiao   

  1. 1. School of Aerospace and Technology,Xidian University,Xi’an,Shaanxi 710071,China; 2. School of Physics and Optoelectronic Engineering,Xidian University,Xi’an,Shaanxi 710071,China; 3. Zhuzhou Rail Tech Electromechanical Technology Co.,Ltd.,Zhuzhou,Hunan 412007,China
  • Received:2018-10-18 Revised:2018-12-26 Online:2019-06-20 Published:2019-07-02

摘要: 对于一端固定、另一端施加正弦激励的弦线振动定解问题,采用分离变量法在共振与非共振两种激励频率下对其进行了求解; 通过对两种不同形式解的研究发现: 对非共振频率激励下的解求极限,亦可得到共振频率激励下的解; 最后通过分析可知: 共振频率激励下的解即为无阻尼条件下的驻波状态解.

关键词: 弦振动方程, 共振频率, 分离变量法, 驻波

Abstract: For the string vibrating problem under the condition that one end is fixed and the other end with sinusoidal incentive,it is solved by the separation of variables under incentive of resonant frequency and non-resonant frequency. Through the study of two different forms of solutions,it is found that the solution under the resonant frequency incentive can be obtained by getting the limit of the solution under non-resonant frequency incentive. Finally,the analysis shows that the solution under resonant frequency incentive is the solution of standing wave state without damping.

Key words: string vibrating equation, resonant frequency, separation of variables, standing wave