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

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170137 ◽  
Author(s):  
Marc Serra-Garcia ◽  
Miguel Molerón ◽  
Chiara Daraio
Keyword(s):  
Energy Transfer ◽  
Frequency Conversion ◽  
Low Frequency ◽  
Multiple Sources ◽  
Localized Modes ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Mechanical ◽  
Mechanical Analogue ◽  
A Chain

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’.

scholarly journals Current-Induced Modulation of the Ocean Wave Spectrum and the Role of Nonlinear Energy Transfer

2008 ◽  
Vol 38 (12) ◽  
pp. 2662-2684 ◽  
Author(s):  
Hitoshi Tamura ◽  
Takuji Waseda ◽  
Yasumasa Miyazawa ◽  
Kosei Komatsu
Keyword(s):  
Energy Transfer ◽  
Numerical Simulations ◽  
The Self ◽  
Current Field ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Transfer ◽  
Stabilization Effect ◽  
Self Stabilization ◽  
Nonlinear Energy

Abstract Numerical simulations were performed to investigate current-induced modulation of the spectral and statistical properties of ocean waves advected by idealized and realistic current fields. In particular, the role of nonlinear energy transfer among waves in wave–current interactions is examined. In this type of numerical simulation, it is critical to treat the nonlinear transfer function (Snl) properly, because a rigorous Snl algorithm incurs a huge computational cost. However, the applicability of the widely used discrete interaction approximation (DIA) method is strictly limited for complex wave fields. Therefore, the simplified RIAM (SRIAM) method is implemented in an operational third-generation wave model. The method approximates an infinite resonant quadruplet with 20 optimized resonance configurations. The performance of the model is assessed by applying it to fetch-limited wave growth and wave propagation against a shear current. Numerical simulations using the idealized current field revealed that the Snl retained spectral form by redistributing the refracted wave energy; this suggests that energy concentration due to ray focusing is dispersed via the self-stabilization effect of nonlinear transfer. A hindcast simulation using wind and current reanalysis data indicated that the difference in the average monthly wave height was substantial and that instantaneous wave–current interactions were highly sensitive to small current structures. Spectral shape was also modulated, and the spatial distributions of the directional bandwidth with or without current data were completely different. Moreover, the self-stabilization effect of the Snl was also confirmed in a realistic situation. These results indicate that a realistic representation of the current field is crucial for high-resolution wave forecasting.

Thermal conductivity, relaxation and low-frequency vibrational mode anomalies in glasses: a model using the Fermi–Pasta–Ulam nonlinear Hamiltonian

2009 ◽  
Vol 367 (1901) ◽  
pp. 3173-3181 ◽  
Author(s):  
J. R. Romero-Arias ◽  
F. Salazar ◽  
G. G. Naumis ◽  
G. Fernandez-Anaya
Keyword(s):  
Thermal Conductivity ◽  
Vibrational Mode ◽  
Low Frequency ◽  
Vibrational Modes ◽  
Conductivity Relaxation ◽  
Cooling Speed ◽  
A Chain ◽  
The Relationship ◽  
Fpu Problem

We present a nonlinear model that allows exploration of the relationship between energy relaxation, thermal conductivity and the excess of low-frequency vibrational modes (LFVMs) that are present in glasses. The model is a chain of the Fermi–Pasta–Ulam (FPU) type, with nonlinear second neighbour springs added at random. We show that the time for relaxation is increased as LFVMs are removed, while the thermal conductivity diminishes. These results are important in order to understand the role of the cooling speed and thermal conductivity during glass transition. Also, the model provides evidence for the fundamental importance of LFVMs in the FPU problem.

scholarly journals Contribution of nonlinearity in tsunami generated by submarine earthquake

2008 ◽  
Vol 14 ◽  
pp. 141-146 ◽  
Author(s):  
M. A. Nosov ◽  
S. V. Kolesov ◽  
A. V. Denisova
Keyword(s):  
Energy Transfer ◽  
Gravitational Waves ◽  
Tsunami Wave ◽  
Low Frequency ◽  
Water Layer ◽  
Additional Contribution ◽  
Tsunami Generation ◽  
Nonlinear Contribution ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

Abstract. Rapid co-seismic bottom displacements during strong submarine earthquake give rise to intensive low-frequency elastic oscillations of water layer. Nonlinear energy transfer from the elastic oscillations to long gravitational waves may provide an additional contribution to tsunami. The nonlinear tsunami generation mechanism is examined analytically. Finiteness of bottom elasticity is taken into account. General parameters responsible for amplitude and energy of the nonlinear contribution to tsunami wave are revealed.

On the Nonlinear Energy Interactions in Harmonically Excited Post-Buckled Flexible Inverted Pendulum in the Presence of Friction

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Vishal Vyas ◽  
Prasanna Gandhi
Keyword(s):  
Energy Transfer ◽  
Inverted Pendulum ◽  
Resonant Mode ◽  
Friction Model ◽  
Low Friction ◽  
Nonlinear Energy Transfer ◽  
Input Side ◽  
Harmonic Resonance ◽  
Nonlinear Energy

Nonlinear energy interaction is a fascinating feature of nonlinear oscillators and has been drawing the attention of researchers since the last few decades. Omnipresent friction in mechanical systems can play a crucial role in modifying these interactions. Using post-buckled flexible inverted pendulum as a candidate system we characterize here, theoretically and experimentally, significant changes in the nonlinear energy transfer in the presence of friction at the input side. Particularly, even with relatively low friction, the energy gets transferred in the higher harmonics of excitation close to a resonant mode as against the transfer to higher modes reported previously. We term this new phenomenon as “excitation harmonic resonance locking.” Theoretical modeling and simulations, considering large deformations, based on assumed modes method, and using a simple friction model reasonably capture the experimental observation. In summary, the paper explicates the role of friction in shifting energy transfer frequencies and can be useful in understanding and designing of oscillators and nonlinear vibrating systems.

scholarly journals Asymptotes of the nonlinear transfer and wave spectrum in the frame of the kinetic equation solution

2018 ◽  
Author(s):  
Vladislav G. Polnikov ◽  
Fangli Qiao ◽  
Yong Teng
Keyword(s):  
Energy Transfer ◽  
Kinetic Equation ◽  
Wave Spectrum ◽  
Low Frequency ◽  
Peak Frequency ◽  
Two Dimensional ◽  
Equation Solution ◽  
Nonlinear Energy Transfer ◽  
The Difference ◽  
Nonlinear Energy

Abstract. The kinetic equation for a gravity wave spectrum is solved numerically to study the high frequencies asymptotes for the one-dimensional nonlinear energy transfer and the variability of spectrum parameters that accompany the long-term evolution of nonlinear waves. The cases of initial two-dimensional spectra S(ω,θ) of modified JONSWAP type with the frequency decay-law S(ω) ~ ω−n (for n = 6, 5, 4 and 3.5) and various initial functions of the angular distribution are considered. It is shown that at the first step of the kinetic equation solution, the nonlinear energy transfer asymptote has the power-like decay-law, Nl(ω) ~ ω−p, with values p ≤ n − 1, valid in cases when n ≥ 5, and the difference, n-p, changes significantly when n approaches 4. On time scales of evolution greater than several thousands of initial wave periods, in every case, a self-similar spectrum Ssf(ω,θ) is established with the frequency decay-law of form S(ω) ~ ω−4. Herein, the asymptote of nonlinear energy transfer becomes negative in value and decreases according to the same law (i.e., Nl(ω) ~ −ω−4). The peak frequency of the spectrum, ωp(t), migrates in time t to the low-frequency region such that the angular and frequency characteristics of the two-dimensional spectrum Ssf(ω,θ) remain constant. However, these characteristics depend on the degree of angular anisotropy of the initial spectrum. The solutions obtained are interpreted, and their connection with the analytical solutions of the kinetic equation by Zakharov and co-authors for gravity waves in water is discussed.

scholarly journals Passive, Nonlinear, Mechanical Structures for Seismic Attenuation

2007 ◽  
Vol 2 (4) ◽  
pp. 290-298 ◽  
Author(s):  
Riccardo DeSalvo
Keyword(s):  
Gravitational Wave ◽  
Nonlinear Response ◽  
Low Frequency ◽  
Space Time ◽  
Seismic Attenuation ◽  
Motion Sensors ◽  
High Quality ◽  
Seismic Motion ◽  
Nonlinear Mechanical ◽  
A Chain

Gravitational wave detectors aim to detect strain perturbations of space-time on the order of 10−21–10−22 at frequencies between 1Hz and a few kHz. This space-time strain, integrated over kilometer scale interferometers, will induce movements of suspended mirrors on the order of 10−18–10−19m. Seismic motion in this frequency band varies between 10−6m and 10−12m. Required seismic attenuation factors, as large as 10−12, by far exceed the performance of motion sensors, and are only obtained by means of a chain of passive attenuators. High quality springs in configurations yielding nonlinear response are used to generate attenuation at low frequency. Similarly, nonlinear mechanisms are used in the horizontal direction. A description of some of these systems and some of the technical challenges that they involve is presented.

Nonlinear energy transfer from low frequency electromagnetic fluctuations to broadband turbulence during edge localized mode crashes

2020 ◽  
Vol 60 (12) ◽  
pp. 124002 ◽  
Author(s):  
Jaewook Kim ◽  
M.J. Choi ◽  
Y.U. Nam ◽  
Hogun Jhang ◽  
J.G. Bak ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Low Frequency ◽  
Nonlinear Energy Transfer ◽  
Edge Localized Mode ◽  
Localized Mode ◽  
Nonlinear Energy

Energy Transfer from High-Frequency to Low-Frequency Modes in Structures

1995 ◽  
Vol 117 (B) ◽  
pp. 186-195 ◽  
Author(s):  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Energy Transfer ◽  
High Frequency ◽  
Large Amplitude ◽  
Low Frequency ◽  
Internal Resonances ◽  
Parametric Resonances ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Low Amplitude

A perspective of the mechanisms by which energy is transferred from high- to low-frequency modes is presented. The focus is on some recent experiments that reveal how a low-amplitude high-frequency excitation can produce a large-amplitude low-frequency response. Such a phenomenon is potentially harmful, if not catastrophic. Specifically, these experiments clarify the role of internal resonances, combination external and parametric resonances, and the interactions among modes of widely spaced frequencies.

Energy Transfer from High-Frequency to Low-Frequency Modes in Structures

1995 ◽  
Vol 117 (B) ◽  
pp. 186-195 ◽  
Author(s):  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Energy Transfer ◽  
High Frequency ◽  
Large Amplitude ◽  
Low Frequency ◽  
Internal Resonances ◽  
Parametric Resonances ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Low Amplitude

A perspective of the mechanisms by which energy is transferred from high- to low-frequency modes is presented. The focus is on some recent experiments that reveal how a low-amplitude high-frequency excitation can produce a large-amplitude low-frequency response. Such a phenomenon is potentially harmful, if not catastrophic. Specifically, these experiments clarify the role of internal resonances, combination external and parametric resonances, and the interactions among modes of widely spaced frequencies.

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