Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences

Djebar Baroudi; I Giorgio; E Turco

doi:10.1007/978-3-030-17747-8_5

Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences

Djebar Baroudi, I Giorgio , E Turco

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

Abstract

In this paper, we show that equilibrium configurations of a clamped beam under distributed load, resembling a curled pending wire—whose existence has been mathematically established—can be obtained experimentally using ‘soft’ beams, i.e. beams for which the ratio between amplitude of the load and bending stiffness is large enough. Moreover, we introduce a Hencky-type discrete model, i.e. a finite dimensional Lagrangian model, for the ‘soft’ Elastica and build a numerical code for determining its motion, in the most general nonlinear regime. This code is able to qualitatively describe observed nonlinear dynamical behavior.

Original language	English
Title of host publication	Recent Developments in the Theory of Shells
Editors	Holm Altenbach, Jacek Chróścielewski, Victor A. Eremeyev, Krzysztof Wiśniewski
Publisher	Springer
Pages	65-78
ISBN (Electronic)	978-3-030-17747-8
ISBN (Print)	978-3-030-17746-1
DOIs	https://doi.org/10.1007/978-3-030-17747-8_5
Publication status	Published - 2019
MoE publication type	A3 Book section, Chapters in research books

Publication series

Name	Advanced Structured Materials
Publisher	Springer
Volume	110

Keywords

Nonlinear beam
Hencky bar-chain
Discrete modelling

Access to Document

10.1007/978-3-030-17747-8_5Licence: Unspecified

Cite this

Baroudi, D., Giorgio , I., & Turco, E. (2019). Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences. In H. Altenbach, J. Chróścielewski, V. A. Eremeyev, & K. Wiśniewski (Eds.), Recent Developments in the Theory of Shells (pp. 65-78). (Advanced Structured Materials; Vol. 110). Springer. https://doi.org/10.1007/978-3-030-17747-8_5

Baroudi, Djebar ; Giorgio , I ; Turco, E. / Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences. Recent Developments in the Theory of Shells . editor / Holm Altenbach ; Jacek Chróścielewski ; Victor A. Eremeyev ; Krzysztof Wiśniewski. Springer, 2019. pp. 65-78 (Advanced Structured Materials).

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title = "Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences",

abstract = "In this paper, we show that equilibrium configurations of a clamped beam under distributed load, resembling a curled pending wire—whose existence has been mathematically established—can be obtained experimentally using {\textquoteleft}soft{\textquoteright} beams, i.e. beams for which the ratio between amplitude of the load and bending stiffness is large enough. Moreover, we introduce a Hencky-type discrete model, i.e. a finite dimensional Lagrangian model, for the {\textquoteleft}soft{\textquoteright} Elastica and build a numerical code for determining its motion, in the most general nonlinear regime. This code is able to qualitatively describe observed nonlinear dynamical behavior.",

keywords = "Nonlinear beam, Hencky bar-chain, Discrete modelling",

author = "Djebar Baroudi and I Giorgio and E Turco",

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Baroudi, D, Giorgio , I & Turco, E 2019, Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences. in H Altenbach, J Chróścielewski, VA Eremeyev & K Wiśniewski (eds), Recent Developments in the Theory of Shells . Advanced Structured Materials, vol. 110, Springer, pp. 65-78. https://doi.org/10.1007/978-3-030-17747-8_5

Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences. / Baroudi, Djebar; Giorgio , I; Turco, E.
Recent Developments in the Theory of Shells . ed. / Holm Altenbach; Jacek Chróścielewski; Victor A. Eremeyev; Krzysztof Wiśniewski. Springer, 2019. p. 65-78 (Advanced Structured Materials; Vol. 110).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

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AU - Giorgio , I

AU - Turco, E

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N2 - In this paper, we show that equilibrium configurations of a clamped beam under distributed load, resembling a curled pending wire—whose existence has been mathematically established—can be obtained experimentally using ‘soft’ beams, i.e. beams for which the ratio between amplitude of the load and bending stiffness is large enough. Moreover, we introduce a Hencky-type discrete model, i.e. a finite dimensional Lagrangian model, for the ‘soft’ Elastica and build a numerical code for determining its motion, in the most general nonlinear regime. This code is able to qualitatively describe observed nonlinear dynamical behavior.

AB - In this paper, we show that equilibrium configurations of a clamped beam under distributed load, resembling a curled pending wire—whose existence has been mathematically established—can be obtained experimentally using ‘soft’ beams, i.e. beams for which the ratio between amplitude of the load and bending stiffness is large enough. Moreover, we introduce a Hencky-type discrete model, i.e. a finite dimensional Lagrangian model, for the ‘soft’ Elastica and build a numerical code for determining its motion, in the most general nonlinear regime. This code is able to qualitatively describe observed nonlinear dynamical behavior.

KW - Nonlinear beam

KW - Hencky bar-chain

KW - Discrete modelling

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SN - 978-3-030-17746-1

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A2 - Chróścielewski, Jacek

A2 - Eremeyev, Victor A.

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PB - Springer

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Baroudi D, Giorgio I, Turco E. Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences. In Altenbach H, Chróścielewski J, Eremeyev VA, Wiśniewski K, editors, Recent Developments in the Theory of Shells . Springer. 2019. p. 65-78. (Advanced Structured Materials). doi: 10.1007/978-3-030-17747-8_5

Large Oscillations Around Curled Equilibrium Configurations of Uniformly Loaded Euler–Bernoulli Beams: Numerical and Experimental Evidences

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