Confinement of vibrations in flexible structures using supplementary absorbers

Dynamic optimization

M. Ouled Chtiba, S. Choura, Sami El-Borgi, A. H. Nayfeh

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.

Original languageEnglish
Pages (from-to)357-376
Number of pages20
JournalJVC/Journal of Vibration and Control
Volume16
Issue number3
DOIs
Publication statusPublished - Mar 2010
Externally publishedYes

Fingerprint

Flexible structures
Damping
Galerkin methods
Equations of motion
Stiffness
Optimal design

Keywords

  • Absorbers
  • Dynamic optimization
  • Galerkin method
  • Vibration confinement

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)
  • Aerospace Engineering
  • Automotive Engineering

Cite this

Confinement of vibrations in flexible structures using supplementary absorbers : Dynamic optimization. / Ouled Chtiba, M.; Choura, S.; El-Borgi, Sami; Nayfeh, A. H.

In: JVC/Journal of Vibration and Control, Vol. 16, No. 3, 03.2010, p. 357-376.

Research output: Contribution to journalArticle

@article{e20da0cef3e240f5ae8f9fd31474ed65,
title = "Confinement of vibrations in flexible structures using supplementary absorbers: Dynamic optimization",
abstract = "We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.",
keywords = "Absorbers, Dynamic optimization, Galerkin method, Vibration confinement",
author = "{Ouled Chtiba}, M. and S. Choura and Sami El-Borgi and Nayfeh, {A. H.}",
year = "2010",
month = "3",
doi = "10.1177/1077546309103423",
language = "English",
volume = "16",
pages = "357--376",
journal = "JVC/Journal of Vibration and Control",
issn = "1077-5463",
publisher = "SAGE Publications Inc.",
number = "3",

}

TY - JOUR

T1 - Confinement of vibrations in flexible structures using supplementary absorbers

T2 - Dynamic optimization

AU - Ouled Chtiba, M.

AU - Choura, S.

AU - El-Borgi, Sami

AU - Nayfeh, A. H.

PY - 2010/3

Y1 - 2010/3

N2 - We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.

AB - We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes.

KW - Absorbers

KW - Dynamic optimization

KW - Galerkin method

KW - Vibration confinement

UR - http://www.scopus.com/inward/record.url?scp=77949897903&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949897903&partnerID=8YFLogxK

U2 - 10.1177/1077546309103423

DO - 10.1177/1077546309103423

M3 - Article

VL - 16

SP - 357

EP - 376

JO - JVC/Journal of Vibration and Control

JF - JVC/Journal of Vibration and Control

SN - 1077-5463

IS - 3

ER -