Breather arrest in a chain of damped oscillators with Hertzian contact

Abstract

Breather propagation in a damped oscillatory chain with Hertzian nearest-neighbour coupling is investigated. The breather propagation exhibits an unusual two-stage pattern. The first stage is characterized by power-law decay of the breather amplitude. This stage extends over finite number of the chain sites. Drastic drop of the breather amplitude towards the end of this finite fragment is referred to as breather arrest. At the second stage, the breather exhibits very small amplitudes with hyper-exponential decay. Numeric results are rationalized by considering a simplified model of two damped linear oscillators coupled by Hertzian contact forces. Initial excitation of one of these oscillators results in a finite number of beating cycles in the system. This simplified model reliably predicts main features of the breather arrest. More general coupling potentials and effect of pre-compression on the breather propagation are also discussed.

Effects of periodic parametric damping and amplitude-modulated signal on vibrational resonance and torus-doubling bifurcations occurrence in an asymmetric mixed Rayleigh-Liénard oscillator

“…The phenomenon of vibrational has received extensive research attention during the last two decades. Due to diverse potential applications of vibrational resonance in many areas of science and modern engineering [37][38][39][40][41], the phenomenon of vibrational resonance has been investigated theoretically and numerically on a diversity of dynamic systems such as asymmetric Duffing oscillator [42], systems with nonlinear damping [43][44][45][46], bistable systems [47][48][49], multistable systems [50,51], excitable systems [52], quintic oscillator [53,54], coupled oscillators [55,56], fractional order oscillators [57,58], biological nonlinear systems [59,60], position dependent mass oscillators [61], parametrically excited systems [61][62][63][64][65], oscillators chains and two-cell cubic autocatalytic reaction-diffusion model [66][67][68][69][70]. Moreover, the phenomenon of vibrational resonance has been explored experimentally [71][72][73][74].…”