A method of finding the principal modes of nonlinear vibration systems and their stabilities
type: Item
instance of: scholarly article
title: A method of finding the principal modes of nonlinear vibration systems and their stabilities
zbMATH Open document ID: 0631.70022
DOI: 10.1007/BF02017401
author: Liansheng Liu
author: Quanzhong Huo
author: Kelei Huang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1987-01-01T00:00:00Z
review text: Für das System ẍ\({}_ i+f_ i(x_ 1,x_ 2,...,x_ n,\dot x_ 1,\dot x_ 2,...,\dot x_ n,t)=0\) mit \(i=1,2,...,n\) kann durch die Substitution \(x_ i=\phi_ i(\xi)=c_{il}\xi +c_{12}\xi^ 2+..\). und Nullsetzen der Koeffizienten des entstehenden Polynoms in \(\xi\), \({\dot \xi}\) und t ein System von algebraischen Gleichungen für die Koeffizienten \(c_{ik}\) abgeleitet werden, dessen reelle Lösungen die Hauptschwingungen des nicht-linearen Systems bestimmen. Einige Spezialfälle, wie lineare, konservative und autonome Systeme, werden kurz behandelt und zwei numerische Beispiele illustrieren den Rechenaufwand.
Mathematics Subject Classification ID: 70K30
zbMATH DE Number: 4026887
zbMATH Keywords: nonlinear vibration
zbMATH Keywords: numerical methods
zbMATH Keywords: stability of principal vibrations
reviewed by: Franz Selig
MaRDI profile type: Publication
cites work: Normal Modes of Nonlinear Dual-Mode Systems
cites work: On Steady-State Harmonic Vibrations of Nonlinear Systems With Many Degrees of Freedom
cites work: On the existence of periodic solutions and normal mode vibrations of nonlinear systems
cites work: Normal modes, uncoupling, and stability for a class of nonlinear oscillators
cites work: The resonant vibration of homogeneous non-linear systems
full work available at URL: https://doi.org/10.1007/bf02017401
OpenAlex ID: W2062694328
description: scientific article; zbMATH DE number 4026887