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 analogue 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.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.

Nonlinear excitations in magnetic lattices with long-range interactions

“…Moreover, the use of magnetic interactions allows exciting applications. They have already been used as a passive mechanism to couple nodes of a lattice for unidirectional wave-guiding [38]; and it has been suggested that magnetic interactions can be used to design novel devices for frequency conversion [39] and shock absorption [36]. In our study, we focus on breathers in a magnetic chain and demonstrate that there is a crossover from exponential decay to algebraic decay in the spatial profile of these breathers.…”

Turing-complete mechanical processor via automated nonlinear system design

“…3a). This type of low-order nonlinear interaction is very common in nature, arising in optomechanical systems [24], magnet lattices [25] and vibrating strings [26] among others.…”

Reversible signal transmission in an active mechanical metamaterial

“…Mechanical metamaterials are artificially constructed and have mechanical properties defined by their structure [1]. Simple metamaterials consist of a one, two, or three-dimensional array of elements connected by links [1][2][3] that may be elastic [4][5][6][7], magnetic [8,9] or electrostatic [4]. Mechanical metamaterials are highly tuneable [10][11][12] and by altering the structure of these elements, and the properties of the links, materials have been developed that selectively transmit signals [13,14], behave as logic gates [5,15] or buckle after the application of external stimulus [2].…”

“…Mechanical metamaterials are artificially constructed and have mechanical properties defined by their structure [1]. Simple metamaterials consist of a one-, two-or three-dimensional array of elements connected by links [1][2][3] that may be elastic [4][5][6][7], magnetic [8,9] or electrostatic [4]. Mechanical metamaterials are highly tuneable [10][11][12] and by altering the 2019 The Author(s) Published by the Royal Society.…”