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Journal of Engineering Materials and Technology | Volume 128 | Issue 3 | SPECIAL SECTION ON DAMPING OF SHAPE MEMORY ALLOYS, COMPOSITES, AND FOAMS
SPECIAL SECTION ON DAMPING OF SHAPE MEMORY ALLOYS, COMPOSITES, AND FOAMS

An Approximated Harmonic Balance Method for Nonlinear Vibration of Viscoelastic Structures

[+] Author and Article Information
El Hassan Boutyour1

Département de Physique Appliquée, Faculté des Sciences et Techniques,  Université Hassan I, BP 577 Settat, Maroc. Laboratoire de Physique et Mécanique des Matériaux, UMR CNRS 7554,  Université Paul Verlaine—Metz, Ile du Saulcy, 57045 Metz Cedex 01 Franceboutyour@lpmm.univ.-metz.fr

El Mostafa Daya

Laboratoire de Physique et Mécanique des Matériaux, UMR CNRS 7554,  Université Paul Verlaine—Metz, Ile du Saulcy, 57045 Metz Cedex 01 France

Lahcen Azrar

Faculté des Sciences et Techniques de Tanger,  Université Abdelmalek Essaadi, BP 416 Tanger, Maroc

Michel Potier-Ferry

Laboratoire de Physique et Mécanique des Matériaux, UMR CNRS 7554,  Université Paul Verlaine—Metz, Ile de Saulcy, 57045 Metz Cedex 01 France

1

Corresponding author: Laboratoire de Physique et Mécanique des Matériaux, UMR CNRS 7554, Université de Metz, ISGMP, Ile du Saulcy 57045 Metz Cedex 01 France.

J. Eng. Mater. Technol 128(3), 330-334 (Mar 09, 2006) (5 pages) doi:10.1115/1.2204944 History: Received September 06, 2005; Revised March 09, 2006
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Citing Articles

In this paper, we deal with the nonlinear vibration of viscoelastic shell structures. Coupling an approximated harmonic balance method with one mode Galerkin’s procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. To show the applicability and the validity of our approach, the amplitude-frequency and the amplitude loss factor relationships are illustrated for a sandwich plate with a viscoelastic central layer and a viscoelastic circular ring.
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Copyright © 2006 by American Society of Mechanical Engineers
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References

1
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2
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4
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Lu, Y. P., Killian, J. W., and Everstine, G. C., 1979, “Vibrations of Three Layered Damped Sandwich Plate Composites,”J. Sound Vib.  [CrossRef], 64 , pp. 63–71.
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Daya, E. M., and Potier-Ferry, M., 2001, “A Numerical Method For Nonlinear Eigenvalue Problem, Application to Vibrations of Viscoelastic Structures,” Comput. Struct., 79 , pp. 533–541.
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Figures

Grahic Jump Location
+Nonlinear free vibration of a viscoelastic circular ring. Modal nonlinear frequencies and modal nonlinear loss factors versus the radial displacement.
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Nonlinear free vibration of a viscoelastic circular ring. Modal nonlinear frequencies and modal nonlinear loss factors versus the radial displacement.
Figure 2

Nonlinear free vibration of a viscoelastic circular ring. Modal nonlinear frequencies and modal nonlinear loss factors versus the radial displacement.

Grahic Jump Location
+Linear and nonlinear frequency-amplitude curves corresponding to the first mode of a simply supported rectangular plate at various excitations
View Large  |  Save Figure  |  Download Slide (.ppt)
Linear and nonlinear frequency-amplitude curves corresponding to the first mode of a simply supported rectangular plate at various excitations
Figure 1

Linear and nonlinear frequency-amplitude curves corresponding to the first mode of a simply supported rectangular plate at various excitations

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