scholarly journals Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170131 ◽  
Author(s):  
Nathan Perchikov ◽  
O. V. Gendelman
Keyword(s):  
Coupled Oscillators ◽  
Energy Exchange ◽  
Initial Conditions ◽  
Complete Analysis ◽  
Slow Flow ◽  
Coupling Energy ◽  
Strongly Nonlinear ◽  
Nonlinear Energy Transfer ◽  
Exchange Regime ◽  
Nonlinear Energy

We consider a system of two linear and linearly coupled oscillators with ideal impact constraints. Primary resonant energy exchange is investigated by analysis of the slow flow using the action–angle (AA) formalism. Exact inversion of the action-energy dependence for the linear oscillator with impact constraints is not possible. This difficulty, typical for many models of nonlinear oscillators, is circumvented by matching the asymptotic expansions for the linear and impact limits. The obtained energy–action relation enables the complete analysis of the slow flow and the accurate description of the critical delocalization transition. The transition from the localization regime to the energy-exchange regime is captured by prediction of the critical coupling value. Accurate prediction of the delocalization transition requires a detailed account of the coupling energy with appropriate redefinition and optimization of the limiting phase trajectory on the resonant manifold. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

Nonlinear Dynamics of Granular Chains

2010 ◽  
Author(s):  
Yuli Starosvetsky ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Traveling Waves ◽  
Equations Of Motion ◽  
Traveling Wave Solutions ◽  
Strongly Nonlinear ◽  
Nonlinear Energy Transfer ◽  
Granular Chains ◽  
Spatial Periodicity ◽  
Analytical Approaches ◽  
Nonlinear Energy

We study strongly nonlinear traveling waves in one-dimensional granular chains with no pre-compression. We directly study the discrete, strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multi-hump traveling wave solutions with arbitrary wavelengths. We develop systematic semi–analytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wavenumber) and energy. Our findings indicate that homogeneous granular chains possess complex nonlinear dynamics, including the capacity for intrinsic nonlinear energy transfer.

scholarly journals Evaluation of Spatial Variation of Nonlinear Energy Transfer by Use of Turbulence Diagnostic Simulator

2013 ◽  
Vol 8 (0) ◽  
pp. 2403070-2403070 ◽  
Author(s):  
Naohiro KASUYA ◽  
Satoru SUGITA ◽  
Makoto SASAKI ◽  
Shigeru INAGAKI ◽  
Masatoshi YAGI ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Spatial Variation ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

scholarly journals Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation.

2006 ◽  
Vol 53 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Ramón Varón ◽  
Matilde E Fuentes ◽  
Manuela García-Moreno ◽  
Francisco Garcìa-Sevilla ◽  
Enrique Arias ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Time Course ◽  
Initial Conditions ◽  
Reaction Scheme ◽  
Complete Analysis ◽  
Zymogen Activation ◽  
Relative Contribution ◽  
Starting Point ◽  
Definition Of

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.

scholarly journals Influence of Accuracy Improvement of Nonlinear Energy Transfer in Wave Model

2009 ◽  
Vol 65 (1) ◽  
pp. 171-175
Author(s):  
Noriaki HASHIMOTO ◽  
Koji KAWAGUCHI ◽  
Katsuyuki SUZUYAMA ◽  
Masaru YAMASHIRO ◽  
Mitsuyoshi KODAMA
Keyword(s):  
Energy Transfer ◽  
Wave Model ◽  
Accuracy Improvement ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

scholarly journals Nonlinear couplings and energy transfers in micro- and nano-mechanical resonators: intermodal coupling, internal resonance and synchronization

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170141 ◽  
Author(s):  
Keivan Asadi ◽  
Jun Yu ◽  
Hanna Cho
Keyword(s):  
Internal Resonance ◽  
Development Stage ◽  
Vibrational Modes ◽  
Mechanical Resonators ◽  
The Past ◽  
Nonlinear Energy Transfer ◽  
Energy Transfers ◽  
Wide Range ◽  
Plate Type ◽  
Nonlinear Energy

Extensive development of micro/nano-electromechanical systems (MEMS/NEMS) has resulted in technologies that exhibit excellent performance over a wide range of applications in both applied (e.g. sensing, imaging, timing and signal processing) and fundamental sciences (e.g. quantum-level problems). Many of these outstanding applications benefit from resonance phenomena by employing micro/nanoscale mechanical resonators often fabricated into a beam-, membrane- or plate-type structure. During the early development stage, one of the vibrational modes (typically the fundamental mode) of a resonator is considered in the design and application. In the past decade, however, there has been a growing interest in using more than one vibrational mode for the enhanced functionality of MEMS/NEMS. In this paper, we review recent research efforts to investigate the nonlinear coupling and energy transfers between multiple modes in micro/nano-mechanical resonators, focusing especially on intermodal coupling, internal resonance and synchronization. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

Clusters of Discrete Breathers in Carbon and Hydrocarbon Nanostructures

2016 ◽  
Vol 845 ◽  
pp. 255-258
Author(s):  
Julia Baimova ◽  
Ivan P. Lobzenko ◽  
Sergey V. Dmitriev
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Energy Exchange ◽  
Initial Conditions ◽  
Initial Amplitude ◽  
Discrete Breathers ◽  
Dynamics Simulations

Clusters of discrete breathers in graphene and graphane are studied by means of molecular dynamics simulations. For both structures, two-breather and three-breather clusters are considered. Energy exchange between discrete breathers in clusters is strongly dependent on the initial conditions such as initial amplitude and phase. Even small changes in these initial parameters can lead to the considerable changes in the behavior or breather clusters.

scholarly journals Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170134 ◽  
Author(s):  
K. Vorotnikov ◽  
M. Kovaleva ◽  
Y. Starosvetsky
Keyword(s):  
Energy Transfer ◽  
Harmonic Excitation ◽  
Two Dimensional ◽  
Theme Issue ◽  
One Dimensional ◽  
Lateral Vibrations ◽  
Nonlinear Energy Transfer ◽  
Energy Exchanges ◽  
Dimensional Models ◽  
Nonlinear Energy

In the present paper, we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two-dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element, subjected to initial or harmonic excitation, to the internal rotator. As for the two-dimensional models (incorporating internal rotators), we will mainly focus on the two special dynamical states, namely a state of the near-complete energy transfer from longitudinal to lateral vibrations of the outer element as well as the state of a permanent, unidirectional energy locking with mild, spatial energy exchanges. In this review, we will discuss the recent theoretical and experimental advancements in the study of essentially nonlinear mechanisms governing the formation and bifurcations of the regimes of intense energy transfer. The present review is composed of two parts. The first part will be mainly devoted to the emergence of resonant energy transfer states in one-dimensional models incorporating internal rotators, while the second part will be mainly concerned with the manifestation of various energy transfer states in two-dimensional ones. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

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