Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance
type: Item
instance of: scholarly article
title: Self-excited oscillators with asymmetric nonlinearities and one-to-two internal resonance
zbMATH Open document ID: 0940.70017
DOI: 10.1023/A:1008360910693
author: S. Natsiavas
author: G. Verros
published in: Nonlinear Dynamics
publication date: 2000-07-24T00:00:00Z
review text: The authors study the dynamic behaviour of mechanical oscillators governed by the equations \(\ddot u_n+\omega^2_n u_n=f_n+ \varepsilon q_n(u_1,u_2, \dot u_1,\dot u_2)\), \((n=1,2)\), and involving quadratic nonlinearities. For small values of \(\varepsilon\), a first order solution is obtained by applying the multiple time scales method; then the stability properties of this solution are determined. As an example, the theory is applied to a simplified model of a metal cutting process, which is studied in details including comparison of numerical results with analytical ones.
reviewed by: Silvio Nocilla
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 1300045
zbMATH Keywords: quadratic nonlinearities
zbMATH Keywords: multiple time scales method
zbMATH Keywords: stability
zbMATH Keywords: metal cutting process
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1300045