Bifurcation of nonlinear normal modes in a class of two degree of freedom systems
type: Item
instance of: scholarly article
title: Bifurcation of nonlinear normal modes in a class of two degree of freedom systems
zbMATH Open document ID: 0793.70014
author: V. Pereyra
published in: Acta Mechanica
publication date: 1994-01-13T00:00:00Z
review text: It is well known that nonlinear forced resonance occurs in the neighborhood of nonlinear normal modes (NNM). Moreover, it was shown that the bifurcations of NNM's affect the topological structure of the resonance curves and the global dynamics. Hence the bifurcation investigation of NNM's is of great practical interest. In this very interesting paper the general class of two degrees of freedom systems with cubic nonlinearities is investigated by a perturbation analysis. The generality of the investigation is possible due to extensive use of computer algebraic methods (MACSYMA). Establishing an approximative first integral, the number and stability of periodic motions is determined. Moreover, the most degenerate bifurcation of periodic motion and a universal unfolding which describes all possible local behavior of periodic motions, is given.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 482333
zbMATH Keywords: MACSYMA
zbMATH Keywords: nonlinear forced resonance
zbMATH Keywords: cubic nonlinearities
zbMATH Keywords: perturbation analysis
zbMATH Keywords: approximative first integral
zbMATH Keywords: stability
zbMATH Keywords: degenerate bifurcation
zbMATH Keywords: universal unfolding
reviewed by: Hans Troger
describes a project that uses: MACSYMA
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 482333