Strongly Nonlinear Beat Phenomena and Energy Exchanges in Weakly Coupled Granular Chains on Elastic Foundations

2012 ◽  
Vol 72 (1) ◽  
pp. 337-361 ◽  
Author(s):  
Yuli Starosvetsky ◽  
M. Arif Hasan ◽  
Alexander F. Vakakis ◽  
Leonid I. Manevitch
Keyword(s):  
Elastic Foundations ◽  
Strongly Nonlinear ◽  
Weakly Coupled ◽  
Granular Chains ◽  
Energy Exchanges

scholarly journals Nonlinear Pulse Equipartition in Weakly Coupled Ordered Granular Chains With No Precompression

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Yuli Starosvetsky ◽  
M. Arif Hasan ◽  
Alexander F. Vakakis
Keyword(s):  
Nonlinear Dynamics ◽  
Solitary Waves ◽  
Practical Significance ◽  
Drastic Reduction ◽  
Strongly Nonlinear ◽  
Localized State ◽  
Weakly Coupled ◽  
Granular Chains ◽  
Initial Impulse ◽  
Primary Pulse

We report on the strongly nonlinear dynamics of an array of weakly coupled, noncompressed, parallel granular chains subject to a local initial impulse. The motion of the granules in each chain is constrained to be in one direction that coincides with the orientation of the chain. We show that in spite of the fact that the applied impulse is applied to one of the granular chains, the resulting pulse that initially propagates only in the excited chain gets gradually equipartitioned between its neighboring chains and eventually in all chains of the array. In particular, the initially strongly localized state of energy distribution evolves towards a final stationary state of formation of identical solitary waves that propagate in each one of the chains. These solitary waves are synchronized and have identical speeds. We show that the phenomenon of primary pulse equipartition between the weakly coupled granular chains can be fully reproduced in coupled binary models that constitute a significantly simpler model that captures the main qualitative features of the dynamics of the granular array. The results reported herein are of major practical significance since it indicates that the weakly coupled array of granular chains is a medium in which an initially localized excitation gets gradually defocused, resulting in drastic reduction of propagating pulses as they are equipartitioned among all chains.

Motion Confinement in a Linear Chain of Coupled Oscillators With a Strongly Nonlinear End Attachment

2003 ◽  
Author(s):  
Leonid Manevitch ◽  
Oleg Gendelman ◽  
Andrey I. Musienko ◽  
Alexander F. Vakakis ◽  
Lawrence Bergman
Keyword(s):  
Coupled Oscillators ◽  
Nonlinear Oscillator ◽  
Linear Chain ◽  
Standing Waves ◽  
Strongly Nonlinear ◽  
Resonant Interactions ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Strongly Nonlinear Oscillator ◽  
Infinite Linear

We study the dynamics of a semi-infinite linear chain of particles that is weakly coupled to a strongly nonlinear oscillator at its free end. We analyze families of localized standing waves situated inside the lower or upper attenuation zones of the linear chain, corresponding to energy predominantly confined in the nonlinear oscillator. These families of standing waves are generated due to resonant interactions between the chain and the nonlinear attachment. A scenario for the realization of energy pumping phenomena in the system under consideration is discussed, and is confirmed by direct numerical simulations of the chain-attachment dynamic interaction.

Strongly nonlinear behavior of granular chains and granular composites

2008 ◽  
Vol 123 (5) ◽  
pp. 3271-3271 ◽  
Author(s):  
Vitali F. Nesterenko ◽  
Eric B. Herbold ◽  
David J. Benson ◽  
Jeonghoon Kim ◽  
Chiara Daraio
Keyword(s):  
Nonlinear Behavior ◽  
Strongly Nonlinear ◽  
Granular Chains ◽  
Granular Composites

Scattering of Solitary Waves and Excitation of Transient Breathers in Granular Media by Light Intruders and No Precompression

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
Yuli Starosvetsky ◽  
K. R. Jayaprakash ◽  
Alexander F. Vakakis
Keyword(s):  
Granular Medium ◽  
Granular Media ◽  
Multiple Scale ◽  
Hertzian Contact ◽  
Reduced Models ◽  
Strongly Nonlinear ◽  
Granular Chains ◽  
Low Amplitude ◽  
Excitation Conditions ◽  
Nonlinear Regimes

We analyze the dynamics of strongly nonlinear granular chains of beads in Hertzian contact with light intruders. We show that the interactions of the light intruders with solitary pulses propagating through the granular medium can be approximately studied by reduced models of the intruders with only their neighboring beads under similar excitation conditions. Studying the reduced models, we identify weakly and strongly nonlinear regimes in the dynamics, depending on the degree of compression between beads and on the occurrence of separation between neighboring beads leading to collisions. We analyze weakly and strongly nonlinear oscillatory regimes of the intruder dynamics by multiple-scale analysis, and by applying special nonsmooth coordinate transformations. When separation between beads occurs, localized transient breathers are excited, corresponding to repeated collisions of an intruder with its neighbors. This leads to high-frequency scattering energy, and to radiation of energy in the granular medium in the form of low-amplitude slowly modulated oscillatory pulses. We find that repeated excitation of localized transient breathers by an array of periodically placed intruders can result in drastic reduction of the amplitude of a solitary wave propagating through the granular medium. This indicates that this type of granular media can be designed as effective shock attenuators.

scholarly journals Strongly nonlinear waves in locally resonant granular chains

Nonlinearity ◽  
2016 ◽  
Vol 29 (11) ◽  
pp. 3496-3527 ◽  
Author(s):  
Lifeng Liu ◽  
Guillaume James ◽  
Panayotis Kevrekidis ◽  
Anna Vainchtein
Keyword(s):  
Nonlinear Waves ◽  
Strongly Nonlinear ◽  
Granular Chains

scholarly journals Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains

2007 ◽  
Vol 98 (16) ◽  
Author(s):  
Alexandre Rosas ◽  
Aldo H. Romero ◽  
Vitali F. Nesterenko ◽  
Katja Lindenberg
Keyword(s):  
Wave Structure ◽  
Strongly Nonlinear ◽  
Granular Chains

scholarly journals A Deep Learning-based approach for forecasting off-gas production and consumption in the blast furnace

2021 ◽  
Author(s):  
Stefano Dettori ◽  
Ismael Matino ◽  
Valentina Colla ◽  
Ramon Speets
Keyword(s):  
Neural Network ◽  
Gas Production ◽  
Real Field ◽  
Short Term ◽  
Strongly Nonlinear ◽  
Echo State Networks ◽  
Production And Consumption ◽  
Analysis Of Results ◽  
Energy Exchanges ◽  
Computing Approach

AbstractThis article presents the application of a recent neural network topology known as the deep echo state network to the prediction and modeling of strongly nonlinear systems typical of the process industry. The article analyzes the results by introducing a comparison with one of the most common and efficient topologies, the long short-term memories, in order to highlight the strengths and weaknesses of a reservoir computing approach compared to one currently considered as a standard of recurrent neural network. As benchmark application, two specific processes common in the integrated steelworks are selected, with the purpose of forecasting the future energy exchanges and transformations. The procedures of training, validation and test are based on data analysis, outlier detection and reconciliation and variable selection starting from real field industrial data. The analysis of results shows the effectiveness of deep echo state networks and their strong forecasting capabilities with respect to standard recurrent methodologies both in terms of training procedures and accuracy.

Dynamics of a Linear Oscillator Coupled to a Bistable Light Attachment: Numerical Study

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Francesco Romeo ◽  
Grigori Sigalov ◽  
Lawrence A. Bergman ◽  
Alex F. Vakakis
Keyword(s):  
Energy Transfer ◽  
Numerical Study ◽  
Energy Levels ◽  
High Energy ◽  
Linear Oscillator ◽  
Efficient Energy Transfer ◽  
Strongly Nonlinear ◽  
Numerical Studies ◽  
Nonlinear Targeted Energy Transfer ◽  
Energy Exchanges

The conservative and dissipative dynamics of a 2DOF, system composed of a grounded linear oscillator coupled to a lightweight mass by means of both strongly nonlinear and linear negative stiffnesses is investigated. Numerical studies are presented aiming to assess the influence of this combined coupling on the transient dynamics. In particular, these studies are focused on passive nonlinear targeted energy transfer from the impulsively excited linear oscillator to the nonlinear bistable lightweight attachment. It is shown that the main feature of the proposed configuration is the ability of assuring broadband efficient energy transfer over a broad range of input energy. Due to the bistability of the attachment, such favorable behavior is triggered by different nonlinear dynamic mechanisms depending on the energy level. For high energy levels, strongly modulated oscillations occur, and the dynamics is governed by fundamental (1:1) and superharmonic (1:3) resonances; for low energy levels, chaotic cross-well oscillations of the nonlinear attachment as well as subharmonic resonances lead to strong energy exchanges between the two oscillators. The results reported in this work indicate that properly designed attachments of this type can be efficient absorbers and dissipators of impulsively induced vibration energy.

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