Nonlinear dynamics of granular chains

Yuli Starosvetsky, Alexander F. Vakakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study strongly nonlinear traveling waves in onedimensional 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.

Original languageEnglish (US)
Title of host publicationASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
Pages913-918
Number of pages6
DOIs
StatePublished - Dec 1 2010
EventASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 - Montreal, QC, Canada
Duration: Aug 15 2010Aug 18 2010

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume5

Other

OtherASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010
CountryCanada
CityMontreal, QC
Period8/15/108/18/10

Fingerprint

Nonlinear Waves
Traveling Wave
Nonlinear Dynamics
Energy Transfer
Complex Dynamics
Traveling Wave Solutions
Homogenization
Periodicity
Governing equation
Equations of Motion
Nonlinear Equations
Continuum
Compression
Wavelength
Nonlinear equations
Energy transfer
Equations of motion
Computing
Arbitrary
Approximation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Starosvetsky, Y., & Vakakis, A. F. (2010). Nonlinear dynamics of granular chains. In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 (pp. 913-918). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 5). https://doi.org/10.1115/DETC2010-29208

Nonlinear dynamics of granular chains. / Starosvetsky, Yuli; Vakakis, Alexander F.

ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010. 2010. p. 913-918 (Proceedings of the ASME Design Engineering Technical Conference; Vol. 5).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Starosvetsky, Y & Vakakis, AF 2010, Nonlinear dynamics of granular chains. in ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010. Proceedings of the ASME Design Engineering Technical Conference, vol. 5, pp. 913-918, ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010, Montreal, QC, Canada, 8/15/10. https://doi.org/10.1115/DETC2010-29208
Starosvetsky Y, Vakakis AF. Nonlinear dynamics of granular chains. In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010. 2010. p. 913-918. (Proceedings of the ASME Design Engineering Technical Conference). https://doi.org/10.1115/DETC2010-29208
Starosvetsky, Yuli ; Vakakis, Alexander F. / Nonlinear dynamics of granular chains. ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010. 2010. pp. 913-918 (Proceedings of the ASME Design Engineering Technical Conference).
@inproceedings{4c287660f8cc4d8faf87b169091f6bf6,
title = "Nonlinear dynamics of granular chains",
abstract = "We study strongly nonlinear traveling waves in onedimensional 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.",
author = "Yuli Starosvetsky and Vakakis, {Alexander F.}",
year = "2010",
month = "12",
day = "1",
doi = "10.1115/DETC2010-29208",
language = "English (US)",
isbn = "9780791844137",
series = "Proceedings of the ASME Design Engineering Technical Conference",
pages = "913--918",
booktitle = "ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010",

}

TY - GEN

T1 - Nonlinear dynamics of granular chains

AU - Starosvetsky, Yuli

AU - Vakakis, Alexander F.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We study strongly nonlinear traveling waves in onedimensional 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.

AB - We study strongly nonlinear traveling waves in onedimensional 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.

UR - http://www.scopus.com/inward/record.url?scp=80054970510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054970510&partnerID=8YFLogxK

U2 - 10.1115/DETC2010-29208

DO - 10.1115/DETC2010-29208

M3 - Conference contribution

AN - SCOPUS:80054970510

SN - 9780791844137

T3 - Proceedings of the ASME Design Engineering Technical Conference

SP - 913

EP - 918

BT - ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010

ER -