Closed-form steady-state solutions for forced vibration of second-order axially moving systems  

作　　者：Jingming FAN Bo CHEN Yinghui LI 

机构地区：[1]School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 610031,China [2]Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province,Southwest Jiaotong University,Chengdu 610031,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2023年第10期1701-1720,共20页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No. 12272323)。

摘　　要：Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.

关 键 词：Green's function axially moving system closed-form solution second-order model forced vibration Laplace transform 

分 类 号：O321[理学—一般力学与力学基础] O326[理学—力学]