Bifurcations and highly nonlinear traveling waves in periodic dimer granular chains

2011 ◽  
Vol 34 (12) ◽  
pp. 1445-1449 ◽  
Author(s):  
Jianwei Shen ◽  
Baojun Miao ◽  
Jigui Luo
Keyword(s):  
Traveling Waves ◽  
Granular Chains ◽  
Highly Nonlinear ◽  
Dimer Granular Chains

Traveling and solitary waves in monodisperse and dimer granular chains

2017 ◽  
Vol 31 (10) ◽  
pp. 1742001 ◽  
Author(s):  
Yuli Starosvetsky ◽  
K. R. Jayaprakash ◽  
Alexander F. Vakakis
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Traveling Waves ◽  
Granular Media ◽  
Equations Of Motion ◽  
Continuum Approximation ◽  
Granular Chains ◽  
Solitary Pulse ◽  
Countably Infinite ◽  
Dimer Granular Chains

We provide a review of propagating traveling waves and solitary pulses in uncompressed one-dimensional ([Formula: see text]) ordered granular media. The first such solution in homogeneous granular media was discovered by Nesterenko in the form of a single-hump solitary pulse with energy-dependent profile and velocity. Considering directly the discrete, strongly nonlinear governing equations of motion of these media (i.e., without resorting to continuum approximation or homogenization), we show the existence of countably infinite families of stable multi-hump propagating traveling waves with arbitrary wavelengths. A semi-analytical approach is used to study the dependence of these waves on spatial periodicity (wavenumber) and energy, and to show that in a certain asymptotic limit, these families converge to the single-hump Nesterenko solitary wave. Then the study is extended in dimer granular chains composed of alternating “heavy” and “light” beads. For a set of specific mass ratios between the light and heavy beads, we show the existence of multi-hump solitary waves that propagate faster than the Nesterenko solitary wave in the corresponding homogeneous granular chain composed of only heavy beads. The existence of these waves has interesting implications in energy transmission in ordered granular chains.

scholarly journals Highly nonlinear solitary waves in periodic dimer granular chains

2008 ◽  
Vol 77 (1) ◽  
Author(s):  
Mason A. Porter ◽  
Chiara Daraio ◽  
Eric B. Herbold ◽  
Ivan Szelengowicz ◽  
P. G. Kevrekidis
Keyword(s):  
Solitary Waves ◽  
Granular Chains ◽  
Highly Nonlinear ◽  
Highly Nonlinear Solitary Waves ◽  
Nonlinear Solitary Waves ◽  
Dimer Granular Chains

Effects of uncertainties on pulse attenuation in dimer granular chains with and without pre-compression

2014 ◽  
Vol 27 (4-5) ◽  
pp. 749-766 ◽  
Author(s):  
M. A. Hasan ◽  
L. Pichler ◽  
Y. Starosvetsky ◽  
D. M. McFarland ◽  
A. F. Vakakis
Keyword(s):  
Granular Chains ◽  
Dimer Granular Chains

scholarly journals PROPAGATION OF HIGHLY NONLINEAR SIGNALS IN A TWO DIMENSIONAL NETWORK OF GRANULAR CHAINS

2008 ◽  
Author(s):  
C. Daraio ◽  
V. F. Nesterenko ◽  
Mark Elert ◽  
Michael D. Furnish ◽  
Ricky Chau ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Dimensional Network ◽  
Granular Chains ◽  
Highly Nonlinear

scholarly journals Demonstration of accelerating and decelerating nonlinear impulse waves in functionally graded granular chains

2018 ◽  
Vol 376 (2127) ◽  
pp. 20170136 ◽  
Author(s):  
Rajesh Chaunsali ◽  
Eunho Kim ◽  
Jinkyu Yang
Keyword(s):  
Functionally Graded ◽  
Contact Forces ◽  
Granular System ◽  
Nonlinear Energy Transfer ◽  
Granular Chains ◽  
Highly Nonlinear ◽  
Impulse Excitation ◽  
Impulse Waves ◽  
Nonlinear Energy ◽  
Stiffness Distribution

We propose a tunable cylinder-based granular system that is functionally graded in its stiffness distribution in space. With no initial compression given to the system, it supports highly nonlinear waves propagating under an impulse excitation. We investigate analytically, numerically and experimentally the ability to accelerate and decelerate the impulse wave without a significant scattering in the space domain. Moreover, the gradient in stiffness results in the scaling of contact forces along the chain. We envision that such tunable systems can be used for manipulating highly nonlinear impulse waves for novel sensing and impact mitigation purposes. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

scholarly journals Periodic Traveling Waves in Diatomic Granular Chains

2013 ◽  
Vol 23 (5) ◽  
pp. 689-730 ◽  
Author(s):  
Matthew Betti ◽  
Dmitry E. Pelinovsky
Keyword(s):  
Traveling Waves ◽  
Periodic Traveling Waves ◽  
Granular Chains

Efficient Energy Transfer and Redirection in Weakly Interacting Granular Lens

2011 ◽  
Author(s):  
Yuli Starosvetsky ◽  
M. A. Hasan ◽  
A. F. Vakakis
Keyword(s):  
Shock Wave ◽  
Energy Transfer ◽  
Mechanical Energy ◽  
Computational Studies ◽  
Efficient Energy Transfer ◽  
Weakly Interacting ◽  
Granular Chains ◽  
Highly Nonlinear ◽  
Challenging Tasks ◽  
Efficient Control

One of the main challenging tasks in the modern design of highly adaptive granular material is in ability to passively control the flow of energy through it by means of trapping, redirection and scattering. In the present work we demonstrate that one of the possible mechanisms to achieve efficient control over the propagating shock wave in the material is the usage of weakly interacting, non-compressed granular lens (granular chains). In the latest computational studies we have demonstrated that the shock waves initially localized on a finite amount of chains may be efficiently redirected to the neighboring granular chains. In this study it is also shown that the amplitude of the shock wave redirected to the neighboring chains may be passively controlled by choosing appropriate parameters of coupling which makes this type of granular structure highly adaptive for the required control of mechanical energy flow. The mechanism for efficient transport of energy from one chain to another are also found. It corresponds to a simple exchange of energy between the weakly interacting granular chains providing equi-partition of Nesterenko solitary waves through the chains. This mechanism of energy transfer and redirection in highly nonlinear granular chains are conceptually new. Analytical and computational studies of all the mechanisms are performed in the present study.

Sign in / Sign up

Export Citation Format

Share Document