Vibrational resonances in 1D Morse and FPU lattices

TL;DR

This paper investigates vibrational mode resonances in 1D Morse and FPU lattices, revealing energy exchange dynamics, mode stability differences, and analytical models that match numerical simulations, advancing understanding of nonlinear lattice vibrations.

Contribution

It provides a detailed analysis of vibrational resonances in 1D Morse and FPU lattices, including analytical descriptions and numerical validation of energy exchange phenomena.

Findings

Resonance energy exchange occurs at specific elongations.

Higher-frequency modes are more stable during resonance.

Analytical models agree well with numerical results.

Abstract

In the present paper the resonances of vibrational modes in one-dimensional random Morse lattice are found and analyzed. The resonance energy exchange is observed at some values of elongation. Resonance $2 \omega_1 = \omega_2$ is investigated in details. The interacting modes are inequivalent: the higher-frequency mode is much more stable in the excited state, i.e. its life-time is larger than the life-time of lower-frequency mode under the resonance conditions. Simple model of two nonlinearly coupled harmonic oscillators is also considered. It allows to get analytical description and to investigate the kinetics and the energy exchange degree vs. such parameters as the resonance detuning and specific energy. The very similar behavior is found in the Morse and the two-oscillatory models, and an excellent agreement between analytical and numerical results is obtained. Analogous resonance phenomena are also found in the random Fermi-Pasta-Ulam lattice under contraction.