Traveling waves for the Mass in Mass model of granular chains

Abstract

In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely a granular chain involving additionally an internal resonator. For these chains, we rigorously establish that under suitable "anti-resonance" conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves bearing non-vanishing tails may exist in the latter case.

References in corpus (6)

• Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
• Compactons and Chaos in Strongly Nonlinear Lattices
• Breathers and surface modes in oscillator chains with Hertzian interactions
• Wave propagation in single column woodpile phononic crystals: Formation of tunable band gaps
• Interaction of Traveling Waves with Mass-With-Mass Defects within a Hertzian Chain
• Traveling Waves and their Tails in Locally Resonant Granular Systems

Cited by in corpus (9)

• Nonlinear Coherent Structures in Granular Crystals
• Wave Propagation in a Strongly Nonlinear Locally Resonant Granular Crystal
• Nanoptera in a Period-2 Toda Chain
• Micropteron traveling waves in diatomic Fermi-Pasta-Ulam-Tsingou lattices under the equal mass limit
• Solitary Waves in Mass-in-Mass Lattices
• Mass-in-Mass Lattices with Small Internal Resonators
• Localized energy absorbers in Hertzian chains
• Breather modes of fully nonlinear mass-in-mass chains
• Metamaterial two-sphere Newton's cradle