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Influence of Loading on Mode Localization in Periodic Structures

[+] Author and Article Information
Reyolando M. L. R. F. Brasil, Carlos E. N. Mazzilli

Department of Structural and Foundations Engineering, Escola Politécnica, da Universidade de São Paulo, CP 61548, 0524-970 - São Paulo, SP, Brazil

Appl. Mech. Rev 48(11S), S132-S137 (Nov 01, 1995) doi:10.1115/1.3005062 History: Online April 29, 2009

Abstract

This paper addresses the problem of the presence of a slightly disordered loading in otherwise ordered periodic structures as an element to trigger the phenomenon of vibration mode localization due to its effect in their stiffness. The sample structures are basically cantilever columns supporting the loads due to large lumped masses in their top which may vary according to a disorder related small parameter. They are connected by very flexible springs. A first series of results deals with a two-degree-of-freedom model where localization is achieved due to loading disorder. The frequencies and displacements show very sharp and nonlinear variation when the small parameter changes slightly around its zero value. The results for this simple model compare well with those of a finite element program developed by the authors. For a more complex example, another model of a rank of six columns is analyzed by the same computer code. A pseudo-random variation of the masses is considered and the resulting vibration modes are compared to those of the ordered structure, which are global in nature and present a sinusoidal spatial distribution. Again, due to mode localization, motions in the perturbed structure are found to be restricted largely to one of the masses.

Copyright © 1995 by The American Society of Mechanical Engineers
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