Homotopy analysis method for multi-degree-of-freedom nonlinear dynamical systems

W. Zhang, Y. H. Qian, M. H. Yao, Siu Kai Lai

Research output: Chapter in book / Conference proceedingConference article published in proceeding or bookAcademic researchpeer-review

Abstract

In reality, the behavior and nature of nonlinear dynamical systems are ubiquitous in many practical engineering problems. The mathematical models of such problems are often governed by a set of coupled second-order differential equations to form multi-degree-of-freedom (MDOF) nonlinear dynamical systems. It is extremely difficult to find the exact and analytical solutions in general. In this paper, the homotopy analysis method is presented to derive the analytical approximation solutions for MDOF dynamical systems. Four illustrative examples are used to show the validity and accuracy of the homotopy analysis and modified homotopy analysis methods in solving MDOF dynamical systems. Comparisons are conducted between the analytical approximation and exact solutions. The results demonstrate that the HAM is an effective and robust technique for linear and nonlinear MDOF dynamical systems. The proof of convergence theorems for the present method is elucidated as well.
Original languageEnglish
Title of host publicationASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
Pages19-28
Number of pages10
Volume3
EditionPARTS A AND B
DOIs
Publication statusPublished - 1 Dec 2010
Externally publishedYes
EventASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 - Montreal, QC, Canada
Duration: 15 Aug 201018 Aug 2010

Conference

ConferenceASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
CountryCanada
CityMontreal, QC
Period15/08/1018/08/10

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

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