Resonant excitation of the bushes of nonlinear vibrational modes in monoatomic chains

Abstract

We present methods for excitation of bushes of nonlinear normal modes in the dynamical system, whose symmetry is described by any point or space group, with the aid of acting on the individual atoms periodic external forces with the frequency of some normal mode of the considered system. It is shown that these methods allow one to excite all bushes of nonlinear modes possible in this system. The application of these methods is illustrated by the excitation of bushes in the chains with the Lennard-Jones interatomic interactions. Each bush corresponds to some exact solution of non-linear equations of motion, which lies on a certain invariant manifold distinguished by symmetry of the considered dynamical system. The value of the concept of bushes of nonlinear modes is determined by the fact that they do not depend on the interatomic interactions, as well as on the degree of nonlinearity. Questions often arising in studying the bush theory, in particular, the problem of their stability, are discussed.