Localized Modes in Periodic Systems With Nonlinear Disorders

[+] Author and Article Information
C. W. Cai

Department of Mechanics, Zhongshan University, Guangzhou, P. R. China

H. C. Chan, Y. K. Cheung

Department of Civil and Structural Engineering, The University of Hong Kong, Hong Kong, China

J. Appl. Mech 64(4), 940-945 (Dec 01, 1997) (6 pages) doi:10.1115/1.2789003 History: Received May 07, 1996; Revised December 03, 1996; Online October 25, 2007


The localized modes of periodic systems with infinite degrees-of-freedom and having one or two nonlinear disorders are examined by using the Lindstedt-Poincare (L-P) method. The set of nonlinear algebraic equations with infinite number of variables is derived and solved exactly by the U-transformation technique. It is shown that the localized modes exist for any amount of the ratio between the linear coupling stiffness kc and the coefficient γ of the nonlinear disordered term, and the nonsymmetric localized mode in the periodic system with two nonlinear disorders occurs as the ratio kc /γ, decreasing to a critical value depending on the maximum amplitude.

Copyright © 1997 by The American Society of Mechanical Engineers
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