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

IF 4.5 2区工程技术 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Mechanics-English Edition Pub Date : 2023-09-30 DOI:10.1007/s10483-023-3035-5

Jingming Fan, Bo Chen, Yinghui Li

{"title":"Closed-form steady-state solutions for forced vibration of second-order axially moving systems","authors":"Jingming Fan, Bo Chen, Yinghui Li","doi":"10.1007/s10483-023-3035-5","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55498,"journal":{"name":"Applied Mathematics and Mechanics-English Edition","volume":"44 10","pages":"1701 - 1720"},"PeriodicalIF":4.5000,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Mechanics-English Edition","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10483-023-3035-5","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

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.

查看原文本刊更多论文

二阶轴向运动系统强迫振动的闭合稳态解

二阶轴向移动系统是动力学领域中常见的模型，如轴向移动的弦、电缆和皮带。在传统的研究工作中，当考虑多个二阶模型的阻尼效应和耦合效应时，很难获得强迫振动的闭合解。本文利用基于拉普拉斯变换的格林函数方法，得到了二阶轴向运动系统强迫振动的闭式解。以轴向移动阻尼弦系统和弹簧连接的多弦系统为例，给出了这些二阶系统的详细求解方法和解析格林函数。通过得到的格林函数也得到了模态函数和频率方程。通过实例验证了结果的可靠性和方便性。本文为二阶轴向运动系统的动力学分析提供了一种系统的分析方法，得到的格林函数适用于不同的二阶系统，而不仅仅适用于弦系统。此外，本文的工作对研究高阶系统的强迫振动也具有积极意义。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Mathematics and Mechanics-English Edition 数学-力学

CiteScore

6.70

自引率

9.10%

发文量

106

审稿时长

2.0 months

期刊介绍： Applied Mathematics and Mechanics is the English version of a journal on applied mathematics and mechanics published in the People''s Republic of China. Our Editorial Committee, headed by Professor Chien Weizang, Ph.D., President of Shanghai University, consists of scientists in the fields of applied mathematics and mechanics from all over China. Founded by Professor Chien Weizang in 1980, Applied Mathematics and Mechanics became a bimonthly in 1981 and then a monthly in 1985. It is a comprehensive journal presenting original research papers on mechanics, mathematical methods and modeling in mechanics as well as applied mathematics relevant to neoteric mechanics.