Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods

Jon Juel Thomsen (Invited author), Iliya I. Blekhman (Invited author)

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control the effective propagation speed of long waves by varying the amplitude of a superimposed high-frequency standing wave. It should be possible to change most properties related to structural stiffness, energy dissipation, and equilibrium states this way, by exploiting the general effects of stiffening, biasing, and smoothening that characterize mechanically high-frequency excited structures. This work explores fundamental issues for spatiotemporally modulated nonlinear materials. First the effective stress-strain relation of a generally nonlinear material with a prescribed HF strain field is derived, discussed, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more realistic case is briefly considered, where the HF standing wave is not given, but is a solution to given external HF input.
Original languageEnglish
Title of host publicationProceedings of COMPDYN 2007 : ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering
Place of PublicationRethymno, Crete
PublisherNational Technical University of Athens
Publication date2007
Publication statusPublished - 2007
EventComputational Methods in Structural Dynamics and Earthquake Engineering - Rethymno, Greece
Duration: 13 Jun 200716 Jun 2007
http://194.42.10.251/compdyn2007/index.html

Conference

ConferenceComputational Methods in Structural Dynamics and Earthquake Engineering
CountryGreece
CityRethymno
Period13/06/200716/06/2007
Internet address

Bibliographical note

12 pages (CD-ROM)

Keywords

  • vibrations
  • effective properties
  • high-frequency
  • elastic wave propagation

Cite this

Thomsen, J. J., & Blekhman, I. I. (2007). Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods. In Proceedings of COMPDYN 2007: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering Rethymno, Crete: National Technical University of Athens.
Thomsen, Jon Juel ; Blekhman, Iliya I. / Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods. Proceedings of COMPDYN 2007: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Rethymno, Crete : National Technical University of Athens, 2007.
@inproceedings{e627dbe27a5d4898845a18ad00de3c2a,
title = "Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods",
abstract = "What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control the effective propagation speed of long waves by varying the amplitude of a superimposed high-frequency standing wave. It should be possible to change most properties related to structural stiffness, energy dissipation, and equilibrium states this way, by exploiting the general effects of stiffening, biasing, and smoothening that characterize mechanically high-frequency excited structures. This work explores fundamental issues for spatiotemporally modulated nonlinear materials. First the effective stress-strain relation of a generally nonlinear material with a prescribed HF strain field is derived, discussed, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more realistic case is briefly considered, where the HF standing wave is not given, but is a solution to given external HF input.",
keywords = "vibrations, effective properties, high-frequency, elastic wave propagation",
author = "Thomsen, {Jon Juel} and Blekhman, {Iliya I.}",
note = "12 pages (CD-ROM)",
year = "2007",
language = "English",
booktitle = "Proceedings of COMPDYN 2007",
publisher = "National Technical University of Athens",

}

Thomsen, JJ & Blekhman, II 2007, Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods. in Proceedings of COMPDYN 2007: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. National Technical University of Athens, Rethymno, Crete, Computational Methods in Structural Dynamics and Earthquake Engineering, Rethymno, Greece, 13/06/2007.

Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods. / Thomsen, Jon Juel (Invited author); Blekhman, Iliya I. (Invited author).

Proceedings of COMPDYN 2007: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Rethymno, Crete : National Technical University of Athens, 2007.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

TY - GEN

T1 - Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods

AU - Thomsen, Jon Juel

AU - Blekhman, Iliya I.

N1 - 12 pages (CD-ROM)

PY - 2007

Y1 - 2007

N2 - What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control the effective propagation speed of long waves by varying the amplitude of a superimposed high-frequency standing wave. It should be possible to change most properties related to structural stiffness, energy dissipation, and equilibrium states this way, by exploiting the general effects of stiffening, biasing, and smoothening that characterize mechanically high-frequency excited structures. This work explores fundamental issues for spatiotemporally modulated nonlinear materials. First the effective stress-strain relation of a generally nonlinear material with a prescribed HF strain field is derived, discussed, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more realistic case is briefly considered, where the HF standing wave is not given, but is a solution to given external HF input.

AB - What are the effective properties of a generally nonlinear material or structure, whose local properties are modulated in both space and time? It has been suggested to use spatiotemporal modulation of structural properties to create materials and structures with adjustable effective properties, and to call these dynamic materials or spatiotemporal composites. Also, according to theoretical predictions, structural nonlinearity enhances the possibilities of achieving specific effective properties. For example, with an elastic rod having cubical elastic nonlinearities, it seems possible to control the effective propagation speed of long waves by varying the amplitude of a superimposed high-frequency standing wave. It should be possible to change most properties related to structural stiffness, energy dissipation, and equilibrium states this way, by exploiting the general effects of stiffening, biasing, and smoothening that characterize mechanically high-frequency excited structures. This work explores fundamental issues for spatiotemporally modulated nonlinear materials. First the effective stress-strain relation of a generally nonlinear material with a prescribed HF strain field is derived, discussed, and exemplified. Then simple approximate analytical expressions are derived for the effective wave speed and natural frequencies for one-dimensional wave propagation in a nonlinear elastic rod, where the spatiotemporal modulation is imposed as a high-frequency standing wave, supposed to be given. Finally the more realistic case is briefly considered, where the HF standing wave is not given, but is a solution to given external HF input.

KW - vibrations

KW - effective properties

KW - high-frequency

KW - elastic wave propagation

M3 - Article in proceedings

BT - Proceedings of COMPDYN 2007

PB - National Technical University of Athens

CY - Rethymno, Crete

ER -

Thomsen JJ, Blekhman II. Using nonlinearity and spatiotemporal property modulation to control effective structural properties: dynamic rods. In Proceedings of COMPDYN 2007: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Rethymno, Crete: National Technical University of Athens. 2007