Free and forced localization in a nonlinear periodic lattice

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Free and forced localized periodic motions in an infinite nonlinear periodic lattice are analytically investigated. The lattice consists of weakly coupled identical masses, each connected to the ground by a nonlinear stiffness. In order to study the localized motions of the discrete system a continuoum approximation is assumed, and the ordinary differential equations of motion are replaced by a single nonlinear partial differential equation. The time-periodic solutions of this equation are then obtained by an averaging method, and their stability is examined using an analytic linearized method. It is shown that localized periodic motions of the lattice correspond to standing solitary solutions of the partial differential equation of the continuous approximation. For the free lattice, localized free motions occur when the coupling stiffnesses forces are much smaller than the nonlinear effects of the grounding stiffnesses. Moreover, these free localized motions are detected in the perfectly periodic nonlinear lattice, i.e., even in the absence of structural disorder (a feature which is an essential prerequisite for linear mode localization). When harmonic forcing is applied to the chain, localized, nonlocalized, and chaotic motions occur, depending on the spatial distribution and the magnitude of the applied loads. A variety of spatially distributed harmonic loads and analytic expressions for the resulting localized motions of the chain are derived.

Original languageEnglish (US)
Title of host publication14th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publicationStructural Dynamics of Large Scale and Complex Systems
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages8
ISBN (Electronic)9780791811764
StatePublished - 1993
EventASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States
Duration: Sep 19 1993Sep 22 1993

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
VolumePart F167972-8


ConferenceASME 1993 Design Technical Conferences, DETC 1993
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation


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