Passive non-linear targeted energy transfer and its applications to vibration absorption: a review

YS Lee, AF Vakakis, LA Bergman… - Proceedings of the …, 2008 - journals.sagepub.com
This review paper discusses recent efforts to passively move unwanted energy from a
primary structure to a local essentially non-linear attachment (termed a non-linear energy …

Sine--Gordon Solitons, Kinks and Breathers as Physical Models of Nonlinear Excitations in Living Cellular Structures

VG Ivancevic, TT Ivancevic - 2013 - projecteuclid.org
Nonlinear space-time dynamics, defined in terms of celebratedsolitonicequations, brings
indispensable tools for understanding, prediction and control of complex behaviors in both …

Irreversible passive energy transfer in coupled oscillators with essential nonlinearity

G Kerschen, YS Lee, AF Vakakis, DM McFarland… - SIAM Journal on Applied …, 2005 - SIAM
We study numerically and analytically the dynamics of passive energy transfer from a
damped linear oscillator to an essentially nonlinear end attachment. This transfer is caused …

A locally stabilized radial basis function partition of unity technique for the sine–Gordon system in nonlinear optics

O Nikan, Z Avazzadeh - Mathematics and Computers in Simulation, 2022 - Elsevier
This paper develops a localized radial basis function partition of unity method (RBF-PUM)
based on a stable algorithm for finding the solution of the sine–Gordon system. This system …

New exact solutions of the coupled sine-Gordon equations in nonlinear optics using the modified Kudryashov method

K Hosseini, P Mayeli, D Kumar - Journal of Modern Optics, 2018 - Taylor & Francis
The main aim of this article is studying the coupled sine-Gordon equations in nonlinear
optics, which describe the propagation of an optical pulse in fibre waveguide. New exact …

New approach to beating phenomenon in coupled nonlinear oscillatory chains

L Manevitch - Archive of Applied Mechanics, 2007 - Springer
We propose an adequate analytical approach to the description of nonlinear vibration with
strong energy exchange between weakly coupled oscillators. The fundamental notion of the …

Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1: 1 resonance captures: Part I

DD Quinn, O Gendelman, G Kerschen… - Journal of Sound and …, 2008 - Elsevier
We study targeted energy transfers and nonlinear transitions in the damped dynamics of a
two degree-of-freedom system of coupled oscillators (a linear oscillator with a lightweight …

Efficiency of targeted energy transfers in coupled nonlinear oscillators associated with 1: 1 resonance captures: Part II, analytical study

TP Sapsis, AF Vakakis, OV Gendelman… - Journal of Sound and …, 2009 - Elsevier
We study targeted energy transfer in a two degree-of-freedom damped system under the
condition of 1: 1 transient resonance capture. The system consists of a linear oscillator …

The use of radial basis functions (RBFs) collocation and RBF-QR methods for solving the coupled nonlinear sine-Gordon equations

M Ilati, M Dehghan - Engineering Analysis with Boundary Elements, 2015 - Elsevier
Radial basis function (RBF) approximation is an extremely powerful tool for solving various
types of partial differential equations, since the method is meshless and can be spectrally …

Numerical study of the one-dimensional coupled nonlinear sine-Gordon equations by a novel geometric meshless method

MS Hashemi - Engineering with Computers, 2021 - Springer
In the paper, we derive a geometric meshless method for coupled nonlinear sine-Gordon
(CNSG) equations. Approximate solutions of the CNSG equations are supposed to be …