Localized Modes in Periodic Systems With Nonlinear Disorders

Abstract

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.