Dynamics and stability of a discrete breather in a harmonically excited chain with vibro-impact on-site potential

Abstract

We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting the possible motion of the masses. Local dissipation is introduced through a non-unit restitution coefficient characterizing the impacts. The system is excited by uniform time-periodic forcing. The present work is aimed to study the existence and stability of similar breathers in the space of parameters, if additional harmonic potentials are introduced. Existence-stability patterns of the breathers in the parameter space and possible bifurcation scenarios are investigated analytically and numerically. In particular, it is shown that the addition of harmonic on-site potential can substantially extend the stability domain, at least close to the anti-continuum limit. This result can be treated as an increase in the robustness of the breather from the perspective of possible practical applications.

Analysis of Vibro-Impact Processes of a Single-Mass System with Viscous Damping and a Single Limiter

“…This was a guidepost which was followed in the research presented in this paper. Characteristics of the horizontal straightline motion of single-mass, one-sided vibro-impact systems are presented in [4], [5], [6], and [7]. A vibro-impact system with two masses moving separately and impacting mutually is presented in [8], while a vibro-impact system with a movable limiter is presented in [9].…”

Periodic Motions of Coupled Impact Oscillators

“…In addition, several analytical approaches have been used to obtain time-periodic solutions formally for different types of piecewiselinear dynamical systems with rigid impacts. One can mention Fourier and Green function methods [4,5,8,17,18,19,23,24,25,31,37], modal decomposition [27,38] and sawtooth time transformations [32]. Most of the results obtained for discrete systems concern impacts localized on a single particle, and different types of waves have been constructed.…”

“…Spatially-localized oscillations (breathers) with a single impacting node have been also studied for different classes of infinite or finite systems. Breather existence and stability has been analyzed for oscillators chains with linear nearest-neighbors coupling and a symmetric local vibroimpact potential (including in some cases a linear component), both for conservative systems [17] and forced systems with dissipative impacts [18,31,37].…”

“…This has been achieved in a number of works in the case of breathers [17,18,37] and for nonsmooth modes close to grazing linear normal modes [27]. In the work [19], the analysis of [31] has been extended to several impacting particles, but the verification of the inequality constraints is still an open problem in that case.…”

“…In this work, we study the existence and stability of time-periodic oscillations in an infinite chain of linearly coupled impact oscillators reminiscent of a model analyzed in [19,31], for rigid impacts without energy dissipation. We show the existence of exact solutions (i.e.…”