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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
Ditaranto, R. A., and Blasingame, W., 1967, “Composite Damping of Vibrating Sandwich Beams,” J. Eng. Ind., 89 , pp. 633–638.
2
Mead, D. J., and Markus, S., 1969, “The Forced Vibration of Three-Layer Damped Sandwich Beam With Arbitrary Boundary Conditions,” J. Sound Vib.  [CrossRef], 10 , pp. 163–175.
3
Yan, M. J., and Dowell, E. H., 1972, “Governing Equations For Vibrating Constrained-Layer Damping Sandwich Plates and Beams,” J. Appl. Mech., 94 , pp. 1041–1047.
4
Oravsky, V., Markus, S., and Simkova, O., 1974, “New Approximate Method of Finding the Loss Factors of a Sandwich Cantilever,” J. Sound Vib., 33 , pp. 335–352.
5
Rao, D. K., 1978, “Frequency and Loss Factors of Sandwich Beams Under Various Boundary Conditions,” J. Mech. Eng. Sci., 20 , pp. 271–282.
6
Sadek, E. A., 1984, “Dynamic Optimisation of a Sandwich Beam,” Comput. Struct., 19 , pp. 605–615.
7
Cupial, P., and Niziol, J., 1995, “Vibration and Damping Analysis of Three-Layered Composite Plate With Viscoelastic Mid-Layer,” J. Sound Vib.  [CrossRef], 183 , pp. 99–114.
8
He, J. F., and Ma, B. A., 1996, “Vibration Analysis of Viscoelastically Damped Sandwich Shells,” Shock Vib. Dig., 3 , pp. 403–417.
9
Hu, Y. C., and Huang, S. C., 2000, “The Frequency Response and Damping Effect of Three-Layer Thin Shell With Viscoelastic Core,” Comput. Struct.  [CrossRef], 76 , pp. 577–591.
10
Kovacs, B., 2002, “Vibration Analysis of a Damped Arch Using Iterative Laminate Model,” J. Sound Vib., 254 , pp. 367–378.
11
Soni, M. L., 1981, “Finite Element Analysis of Viscoelastically Damped Sandwich Structures,” Shock Vib. Dig., 55 , pp. 97–109.
12
Ma, B. A., and He, J. F., 1992, “A Finite Element Analysis of Viscoelastically Damped Sandwich Plates,” J. Sound Vib., 152 , pp. 107–123.
13
Rikards, R., Chate, A., and Barkanov, E., 1993, “Finite Element Analysis of Damping the Vibrations of Laminated Composites,” Comput. Struct., 47 , pp. 1005–1015.
14
Johnson, C. D., Kienholz, D. A., and Rogers, L. C., 1981, “Finite Element Prediction of Damping in Beams With Constrained Viscoelastic Layer,” Shock Vib. Dig., 51 , pp. 71–81.
15
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.
16
Sainsbury, M. G., and Zhang, Q. J., 1999, “The Galerkin Element Method Applied to the Vibration of Damped Sandwich Beams,” Comput. Struct., 71 , pp. 239–256.
17
Ramesh, T. C., and Ganesan, N., 1994, “Finite Element Analysis of Conical Shells With a Constrained Viscoelastic Layer,” J. Sound Vib., 171 , pp. 577–601.
18
Baber Thomas, T., Maddox Richard, A., and Orozco Carlos, E., 1998, “A Finite Element Model For Harmonically Excited Viscoelastic Sandwich Beams,” Comput. Struct., 66 , pp. 105–113.
19
Alam, N., and Asnani, N. T., 1984, “Vibration and Damping of Multi Layered Cylindrical Shell. Part I and II,” AIAA J., 22 , pp. 803–810;Alam, N., and Asnani, N. T., 1984, “Vibration and Damping of Multi Layered Cylindrical Shell. Part II,” AIAA J., 22 , pp. 975–981.
20
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.
21
Chen, X., Chen, H. L., and Le, H., 1999, “Damping Prediction of Sandwich Structures by Order-Reduction-Iteration Approach,” J. Sound Vib., 222 , pp. 803–812.
22
Daya, E. M., and Potier-Ferry, M., 2002, “A Shell Finite Element For Viscoelastically Damped Sandwich Structures,” Revue Européenne des Eléments finis, 11 , pp. 39–56.
23
Lee, H.-H., 1998, “Non-Linear Vibration of a Multilayer Sandwich Beam With Viscoelastic Layers,” J. Sound Vib., 216 , pp. 601–621.
24
Daya, E. M., Azrar, L., and Potier-Ferry, M., 2003, “An Amplitude Equation For the Non-Linear Vibration of Viscoelastically Damped Sandwich Beams,” J. Sound Vib., 271 , pp. 789–813.
25
Patel, B. P., Ganapathi, M., Makhecha, D. P., and Shah, P., 2003, “Large Amplitude Free Flexural Vibration of Rings Using Finite Element Approach,” Int. J. Non-Linear Mech., 37 , pp. 911–921.
26
Ganapathi, M., Patel, B. P., Boisse, P., and Polit, O., 1999, “Flexural Loss Factors of Sandwich and Laminated Beams Using Linear and Nonlinear Dynamic Analysis,” Composites, Part B, 30 , pp. 245–256.
27
Nayfeh, A. H., and Mook, D. T., 1979, "Non Linear Oscillations", Wiley, New York.
28
Brush, D. O., and Almroth, B. O., 1975, "Buckling of Bars, Plate and Shells", McGraw-Hill, New York.

Figures

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

Grahic Jump Location
+Nonlinear free vibration of a viscoelastic circular ring. Modal nonlinear frequencies and modal nonlinear loss factors versus the radial displacement.
View Large  |  Save Figure  |  Download Slide (.ppt)
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.

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