Forced localization in a periodic chain of nonlinear oscillators
type: Item
instance of: scholarly article
title: Forced localization in a periodic chain of nonlinear oscillators
zbMATH Open document ID: 0848.70016
DOI: 10.1016/0020-7462(94)90013-2
author: A. F. Vakakis
author: Melvin E. King
author: Arne J. Pearlstein
published in: International Journal of Non-Linear Mechanics
publication date: 1996-11-04T00:00:00Z
review text: Forced localization is considered in a periodic system consisting of an infinite number of particles, each coupled to adjacent particles by linear springs and connected to a rigid foundation by a nonlinear stiffness. A ``continuum approximation'' is used to reduce the infinite set of ordinary differential equations of motion to a single approximate, nonlinear partial differential equation. The structure of the propagation zones and the attenuation zones of the linearized system is found to effect the nonlinear localization. Harmonic excitations with general spatial distributions are considered, and the localized responses of the chain are studied using exact and asymptotic techniques. Depending on the specified spatial form of the excitation, localized, non-localized or even spatially chaotic responses of the chain can be realized. The theoretical predictions are verified by direct numerical solutions of the equations of motion.
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 699175
zbMATH Keywords: asymptotic technique
zbMATH Keywords: spatially chaotic response
zbMATH Keywords: continuum approximation
zbMATH Keywords: infinite number of particles
zbMATH Keywords: linear springs
zbMATH Keywords: rigid foundation
zbMATH Keywords: nonlinear stiffness
zbMATH Keywords: nonlinear partial differential equation
zbMATH Keywords: propagation zones
zbMATH Keywords: attenuation zones
reviewed by: Bozhidar Cheshankov
MaRDI profile type: Publication
full work available at URL: 0020-7462(94)90013-2
OpenAlex ID: W2076877077
description: scientific article; zbMATH DE number 699175