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

Breathers in lattices with alternating strain-hardening and strain-softening interactions

This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain hardening and strain softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving, are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a nonlinear Schrödinger equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.

Dynamics of time-modulated, nonlinear phononic lattices

The propagation of acoustic and elastic waves in time-varying, spatially homogeneous media can exhibit different phenomena when compared to traditional spatially varying, temporally homogeneous media. In the present work, the response of a one-dimensional phononic lattice with time-periodic elastic properties is studied with experimental, numerical and theoretical approaches in both linear and nonlinear regimes. The system consists of repelling magnetic masses with grounding stiffness controlled by electrical coils driven with electrical signals that vary periodically in time. For small-amplitude excitation, in agreement with linear theoretical predictions, wave-number band gaps emerge. The underlying instabilities associated to the wave-number band gaps are investigated with Floquet theory and the resulting parametric amplification is observed in both theory and experiments. In contrast to genuinely linear systems, large-amplitude responses are stabilized via the nonlinear nature of the magnetic interactions of the system, and results in a family of nonlinear time-periodic states. The bifurcation structure of the periodic states is studied. It is found the linear theory correctly predicts parameter values from which the time-periodic states bifurcate from the zero state. In the presence of an external drive, the parametric amplification induced by the wave-number band gap can lead to bounded and stable responses that are temporally quasiperiodic. Controlling the propagation of acoustic and elastic waves by balancing nonlinearity and external modulation offers a new dimension in the realization of advanced signal processing and telecommunication devices. For example, it could enable time-varying, cross-frequency operation, mode- and frequency-conversion, and signal-to-noise ratio enhancements.

Extreme Frequency Conversion from Soliton Resonant Interactions

We present a metastructure architecture with a bistable microstructure that enables extreme broadband frequency conversion. We use numerical and experimental tools to unveil the relationship between input excitations at the unit cell level and output responses at the macrostructural level. We identify soliton-lattice mode resonances resulting in input-independent energy transfer into desired metabeam vibration modes as long as transition waves are triggered within the metastructure. We observe both low-to-high and high-to-low incommensurate frequency interactions in the metabeams, thus enabling energy exchange between bands 2 orders of magnitude apart. This behavior generalizes fluxon-cavity mode resonance in superconducting electronics, providing a general method to extreme frequency conversion in mechanics. Importantly, the introduced architecture allows for expanding the metamaterials design paradigm by fundamentally breaking the dependence of macroscopic dynamics on the unit cell properties. The resulting input-independent nature implies potential applications in broadband frequency regulation and energy transduction.

Turing-complete mechanical processor via automated nonlinear system design

Nanomechanical computers promise a greatly improved energetic efficiency compared to their electrical counterparts. However, progress towards this goal is hindered by a lack of modular components, such as logic gates or transistors, and systematic design strategies. This article describes a universal logic gate implemented as a nonlinear mass-spring-damper model, followed by an automated method to translate computations, expressed as source code of arbitrary complexity, into combinations of this basic building block. The proposed approach is validated numerically in two steps: First, a set of discrete models are generated from code. The models implement computations with increasing complexity, starting by a simple adder and ending in a eight-bit Turing complete mechanical processor. Then the models are forward integrated to demonstrate their computing performance. The processor is validated by executing the Erathostenes' sieve algorithm to mechanically compute prime numbers.

Reversible signal transmission in an active mechanical metamaterial

Mechanical metamaterials are designed to enable unique functionalities, but are typically limited by an initial energy state and require an independent energy input to function repeatedly. Our study introduces a theoretical active mechanical metamaterial that incorporates a biological reaction mechanism to overcome this key limitation of passive metamaterials. Our material allows for reversible mechanical signal transmission, where energy is reintroduced by the biologically motivated reaction mechanism. By analysing a coarse-grained continuous analogue of the discrete model, we find that signals can be propagated through the material by a travelling wave. Analysis of the continuum model provides the region of the parameter space that allows signal transmission, and reveals similarities with the well-known FitzHugh-Nagumo system. We also find explicit formulae that approximate the effect of the time scale of the reaction mechanism on the signal transmission speed, which is essential for controlling the material.

Introduction to a topical issue 'nonlinear energy transfer in dynamical and acoustical Systems'

This topical issue is devoted to recent developments in the broader field of energy transfer across scales in nonlinear dynamical and acoustical systems. Nonlinear energy transfers are common in Nature, with perhaps the most famous example being energy cascading from large to small length scales in turbulent flows. Yet nonlinearity has been traditionally perceived either as an unavoidable nuisance or as an unwelcome design restriction in engineering systems. Nowadays, however, this trend is reversing, with nonlinear phenomena being intensely studied in diverse disciplines. Furthermore, strong nonlinearity is now intentionally used and explored in a variety of mechanical and physical settings, such as granular media, acoustic metamaterials, nonlinear energy sinks, essentially nonlinear and nonlocal lattices, vibro-impact oscillators, vibration and shock isolation systems, nanotechnology, biomimetic systems, microelectronics, energy harvesters and in other applications. This topical issue is an attempt to document in a single volume some of these recent research developments, in order to establish a common basis and provide motivation and incentive for further development. The aim is to discuss and compare theoretical and experimental approaches pursued by research groups in different areas, and describe the state of the art of nonlinear energy transfer phenomena in an as broad as possible range of applications of current interest.This article is part of the theme issue 'Nonlinear energy transfer in dynamical and acoustical systems'.