Tunable, synchronized frequency down-conversion in magnetic lattices with defects

Abstract

We study frequency conversion in nonlinear mechanical lattices, focusing on a chain of magnets as a model system. We show that by inserting mass defects at suitable locations, we can introduce localized vibrational modes that nonlinearly couple to extended lattice modes. The nonlinear interaction introduces an energy transfer from the high-frequency localized modes to a low-frequency extended mode. This system is capable of autonomously converting energy between highly tunable input and output frequencies, which need not be related by integer harmonic or subharmonic ratios. It is also capable of obtaining energy from multiple sources at different frequencies with a tunable output phase, due to the defect synchronization provided by the extended mode. Our lattice is a purely mechanical analog of an opto-mechanical system, where the localized modes play the role of the electromagnetic field, and the extended mode plays the role of the mechanical degree of freedom.

References in corpus (13)

• Cavity Optomechanics
• Cavity Optomechanics
• Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5
• Energy trapping and shock disintegration in a composite granular medium
• Strongly nonlinear waves in a chain of Teflon beads
• Discrete Breathers in One-Dimensional Diatomic Granular Crystals
• Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
• Tunable Vibrational Band Gaps in One-Dimensional Diatomic Granular Crystals with Three-Particle Unit Cells
• Experimental Realization of a Nonlinear Acoustic Lens with a Tunable Focus
• Tunable magneto-granular phononic crystals
• Shock and Rarefaction Waves in Generalized Hertzian Contact Models
• A mechanical autonomous stochastic heat engine
• Extraordinary stiffness tunability through thermal expansion of nonlinear defect modes

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• Design, Dynamics, and Dissipation of a Torsional-Magnetic Spring Mechanism
• Breathers in lattices with alternating strain-hardening and strain-softening interactions
• Natural Frequency Dependency of Magneto-Mechanical Resonators on Magnet Distance