Forced localization in a periodic chain of nonlinear oscillators
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.
scientific article; zbMATH DE number 699175