Non-linear vibrations of sandwich viscoelastic shells

Lahcen Benchouaf; El Hassan Boutyour; El Mostafa Daya; Michel Potier-Ferry

doi:10.1016/j.crme.2017.12.013

Non-linear vibrations of sandwich viscoelastic shells

Lahcen Benchouaf ¹ ; El Hassan Boutyour ¹; El Mostafa Daya ²; Michel Potier-Ferry ²

¹ Laboratory of Mechanics, Energetics, Electronics & Telecommunications, Department of Applied Physics, Faculty of Sciences and Technology, Hassan 1st University, PO Box 577, Settat, Morocco
² Laboratoire d'étude des microstructures et de mécanique des matériaux (LEM3), UMR CNRS 7239, Université de Lorraine, Metz, France

Comptes Rendus. Mécanique, Volume 346 (2018) no. 4, pp. 308-319.

Abstract

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the 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. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

Received: 2017-10-09
Accepted: 2017-12-04
Published online: 2018-02-23

DOI: 10.1016/j.crme.2017.12.013

Mots-clés : Non-linear vibration, Viscoelastic, Sandwich, Harmonic balance method, Eigenvalue, Loss factor

Author's affiliations:

Lahcen Benchouaf ¹; El Hassan Boutyour ¹; El Mostafa Daya ²; Michel Potier-Ferry ²

¹ Laboratory of Mechanics, Energetics, Electronics & Telecommunications, Department of Applied Physics, Faculty of Sciences and Technology, Hassan 1st University, PO Box 577, Settat, Morocco
² Laboratoire d'étude des microstructures et de mécanique des matériaux (LEM3), UMR CNRS 7239, Université de Lorraine, Metz, France

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     author = {Lahcen Benchouaf and El Hassan Boutyour and El Mostafa Daya and Michel Potier-Ferry},
     title = {Non-linear vibrations of sandwich viscoelastic shells},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {308--319},
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     volume = {346},
     number = {4},
     year = {2018},
     doi = {10.1016/j.crme.2017.12.013},
     language = {en},
}

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Lahcen Benchouaf; El Hassan Boutyour; El Mostafa Daya; Michel Potier-Ferry. Non-linear vibrations of sandwich viscoelastic shells. Comptes Rendus. Mécanique, Volume 346 (2018) no. 4, pp. 308-319. doi : 10.1016/j.crme.2017.12.013. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.12.013/

References
Cited by

[1] R.A. Ditaranto; W. Blasingame Composite damping of vibrating sandwich beams, J. Eng. Ind., Volume 89 (1967) no. 4, pp. 633-638

[2] D.J. Mead; S. Markus The forced vibration of three-layer damped sandwich beam with arbitrary boundary conditions, J. Sound Vib., Volume 10 (1969), pp. 163-175

[3] M.J. Yan; E.H. Dowell Governing equations for vibrating constrained-layer damping sandwich plates and beams, J. Appl. Mech., Volume 94 (1972), pp. 1041-1047

[4] V. Oravsky; S. Markus; O. Simkova New approximate method of finding the loss factors of a sandwich cantilever, J. Sound Vib., Volume 33 (1974), pp. 335-352

[5] D.K. Rao Frequency and loss factors of sandwich beams under various boundary conditions, J. Mech. Eng. Sci., Volume 20 (1978) no. 5, pp. 271-282

[6] E.A. Sadek Dynamic optimisation of a sandwich beam, Comput. Struct., Volume 19 (1984) no. 4, pp. 605-615

[7] P. Cupial; J. Niziol Vibration and damping analysis of three-layered composite plate with viscoelastic mid-layer, J. Sound Vib., Volume 183 (1995) no. 1, pp. 99-114

[8] J.F. He; B.A. Ma Vibration analysis of viscoelastically damped sandwich shells, Shock Vib. Bull., Volume 3 (1996) no. 6, pp. 403-417

[9] Y.C. Hu; S.C. Huang The frequency response and damping effect of three-layer thin shell with viscoelastic core, Comput. Struct., Volume 76 (2000), pp. 577-591

[10] B. Kovâcs Vibration analysis of a damped arch using iterative laminate model, J. Sound Vib., Volume 254 (2002) no. 2, pp. 367-378

[11] M.L. Soni Finite element analysis of viscoelastically damped sandwich structures, Shock Vib. Bull., Volume 55 (1981) no. 1, pp. 97-109

[12] B.A. Ma; J.F. He A finite element analysis of viscoelastically damped sandwich plates, J. Sound Vib., Volume 152 (1992), pp. 107-123

[13] R. Rikards; A. Chate; E. Barkanov Finite element analysis of damping the vibrations of laminated composites, Comput. Struct., Volume 47 (1993) no. 6, pp. 1005-1015

[14] C.D. Johnson; D.A. Kienholz; L.C. Rogers Finite element prediction of damping in beams with constrained viscoelastic layer, Shock Vib. Bull., Volume 51 (1981) no. 1, pp. 71-81

[15] Y.P. Lu; J.W. Killian; G.C. Everstine Vibrations of three layered damped sandwich plate composites, J. Sound Vib., Volume 64 (1979) no. 1, pp. 63-71

[16] M.G. Sainsbury; Q.J. Zhang The Galerkin element method applied to the vibration of damped sandwich beams, Comput. Struct., Volume 71 (1999), pp. 239-256

[17] T.C. Ramesh; N. Ganesan Finite element analysis of conical shells with a constrained viscoelastic layer, J. Sound Vib., Volume 171 (1994) no. 5, pp. 577-601

[18] T.T. Baber; R.A. Maddox; C.E. Orozco A finite element model for harmonically excited viscoelastic sandwich beams, Comput. Struct., Volume 66 (1998) no. 1, pp. 105-113

[19] N. Alam; N.T. Asnani Vibration and damping of multi layered cylindrical shell. Part I and II, AIAA J., Volume 22 (1984), pp. 803-810 (975–981)

[20] E.M. Daya; M. Potier-Ferry A numerical method for nonlinear eigenvalue problem, application to vibrations of viscoelastic structures, Comput. Struct., Volume 79 (2001) no. 5, pp. 533-541

[21] X. Chen; H.L. Chen; H. Le Damping prediction of sandwich structures by order-reduction-iteration approach, J. Sound Vib., Volume 222 (1999) no. 5, pp. 803-812

[22] E.M. Daya; M. Potier-Ferry A shell finite element for viscoelastically damped sandwich structures, Rev. Eur. Elém. Fin., Volume 11 (2002) no. 1, pp. 39-56

[23] H.-H. Lee Non-linear vibration of a multilayer sandwich beam with viscoelastic layers, J. Sound Vib., Volume 216 (1998) no. 4, pp. 601-621

[24] E.M. Daya; L. Azrar; M. Potier-Ferry An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams, J. Sound Vib., Volume 271 (2003) no. 3, pp. 789-813

[25] B.P. Patel; M. Ganapathi; D.P. Makhecha; P. Shah Large amplitude free flexural vibration of rings using finite element approach, Int. J. Non-Linear Mech., Volume 37 (2003), pp. 911-921

[26] M. Ganapathi; B.P. Patel; P. Boisse; O. Polit Flexural loss factors of sandwich and laminated beams using linear and nonlinear dynamic analysis, Composites, Part B, Eng., Volume 30 (1999), pp. 245-256

[27] E.H. Boutyour; E.M. Daya; M. Potier-Ferry A harmonic balance method for the non-linear vibration of viscoelastic shell, C. R. Mecanique, Volume 334 (2006), pp. 68-73

[28] F. Boumediene; J.M. Cadou; L. Duigou; E.M. Daya A reduction model for eigensolutions of damped viscoelastic sandwich structures, Mech. Res. Commun., Volume 57 (2014), pp. 74-81

[29] F. Boumediene; E.M. Daya; J.M. Cadou; L. Duigou Forced harmonic response of viscoelastic sandwich beams by a reduction method, Mech. Adv. Mat. Struct., Volume 23 (2016) no. 11, pp. 1290-1299

[30] M. Amabili Nonlinear vibrations of viscoelastic rectangular plates, J. Sound Vib., Volume 362 (2016) no. 3, pp. 142-156

[31] K.G. Lougou; H. Boudaoud; E.M. Daya; L. Azrar Vibration modeling of large repetitive sandwich structures with viscoelastic core, Mech. Adv. Mat. Struct., Volume 23 (2016) no. 4, pp. 458-466

[32] K. Lampoh; I. Charpentier; E.M. Daya Erratum to “Eigenmode sensitivity of damped sandwich structures” [C. R. Mecanique 342 (2014) 700–705], C. R. Mecanique, Volume 343 (2015) no. 3, p. 246

[33] I. Elkhaldi; I. Charpentier; E.M. Daya A gradient method for viscoelastic behaviour identification of damped sandwich structures, C. R. Mecanique, Volume 340 (2012) no. 8, pp. 619-623

[34] A.H. Nayfeh; D.T. Mook Nonlinear Oscillations, Wiley, New York, 1979

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