非线性振动系统的简化哈密顿频幅公式

IF 10.1 2区工程技术 Q1 ENGINEERING, MECHANICAL

Facta Universitatis-Series Mechanical Engineering Pub Date : 2022-07-28 DOI:10.22190/fume220420023m

Hong-ping Ma

{"title":"非线性振动系统的简化哈密顿频幅公式","authors":"Hong-ping Ma","doi":"10.22190/fume220420023m","DOIUrl":null,"url":null,"abstract":"The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory. ","PeriodicalId":51338,"journal":{"name":"Facta Universitatis-Series Mechanical Engineering","volume":null,"pages":null},"PeriodicalIF":10.1000,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"SIMPLIFIED HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR VIBRATION SYSTEMS\",\"authors\":\"Hong-ping Ma\",\"doi\":\"10.22190/fume220420023m\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory. \",\"PeriodicalId\":51338,\"journal\":{\"name\":\"Facta Universitatis-Series Mechanical Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":10.1000,\"publicationDate\":\"2022-07-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Facta Universitatis-Series Mechanical Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.22190/fume220420023m\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Facta Universitatis-Series Mechanical Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.22190/fume220420023m","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}

引用次数: 24

摘要

基于哈密顿的频率公式被誉为前所未有的成功，因为它以简单的计算直观地洞察了复杂的非线性振动系统。本文对该配方进行了系统分析，并提出了两种简化配方。以三次五次Duffing振荡器为例，计算简单，精度高。它可以作为许多其他应用的范例，一步求解过程清理了非线性振动理论的道路。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

SIMPLIFIED HAMILTONIAN-BASED FREQUENCY-AMPLITUDE FORMULATION FOR NONLINEAR VIBRATION SYSTEMS

The Hamiltonian-based frequency formulation has been hailed as an unprecedented success for it gives a straightforward insight into a complex nonlinear vibration system with simple calculation. This paper gives a systematical analysis of the formulation, and two simplified formulations are suggested. The cubic-quintic Duffing oscillator is used as an example to show extremely simple calculation and remarkable accuracy. It can be used as a paradigm for many other applications, and the one-step solving process has cleaned up the road of the nonlinear vibration theory.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Facta Universitatis-Series Mechanical Engineering ENGINEERING, MECHANICAL-

CiteScore

14.40

自引率

2.50%

发文量

审稿时长

6 weeks

期刊介绍： Facta Universitatis, Series: Mechanical Engineering (FU Mech Eng) is an open-access, peer-reviewed international journal published by the University of Niš in the Republic of Serbia. It publishes high-quality, refereed papers three times a year, encompassing original theoretical and/or practice-oriented research as well as extended versions of previously published conference papers. The journal's scope covers the entire spectrum of Mechanical Engineering. Papers undergo rigorous peer review to ensure originality, relevance, and readability, maintaining high publication standards while offering a timely, comprehensive, and balanced review process.