Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta's Substitution

Y. Y. Lee

doi:10.1155/2016/3462643

Author(s)

Y. Y. Lee

Related Research Unit(s)

Department of Architecture and Civil Engineering

Detail(s)

Original language	English
Article number	3462643
Journal / Publication	Shock and Vibration
Volume	2016
Publication status	Published - Jul 2016

Link(s)

DOI	DOI https://doi.org/10.1155/2016/3462643 Final Published version
	Check@CityULib
Attachment(s)	Documents 6985271.pdf Final Published version, 1.51 MB, PDF Publisher's Copyright Statement This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84955441455&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(27baba5a-203e-49d1-982a-e4e9794cdf56).html

Abstract

This paper presents a modified harmonic balance solution method incorporated with Vieta's substitution technique for nonlinear multimode damped beam vibration. The aim of the modification in the solution procedures is to develop the analytic formulations, which are used to calculate the vibration amplitudes of a nonlinear multimode damped beam without the need of nonlinear equation solver for the nonlinear algebraic equations generated in the harmonic balance processes. The result obtained from the proposed method shows reasonable agreement with that from a previous numerical integration method. In general, the results can show the convergence and prove the accuracy of the proposed method.