journal article·2021-10Open access

A finite element approach for the static and vibration analyses of functionally graded material viscoelastic sandwich beams with nonlinear material behavior

Kouami Koutoati, Foudil Mohri, El Mostafa Daya, Erasmo Carrera

Abstract

Abstract A beam finite element model is proposed for the static and free vibration analyses of FGM sandwich beams with viscoelastic nonlinear material behavior . In the analysis, zigzag theory is adopted for the displacement fields. The damping results from the shear properties of the viscoelastic layer and its low stiffness. Timoshenko 1st order and Reddy’s higher order shear models are implemented for static and vibration behaviors. Various viscoelastic frequency-dependent laws are considered. The resulting stiffness matrix is nonlinear and is frequency dependent. Solutions are possible according to a powerful asymptotic method combined with recent method for the power series terms. The efficiency of the present model is proven through simulations using 3D volume elements of Abaqus code, where new module for viscoelastic FGM materials is now available. The effects of power law index and boundary conditions on static, vibration and the damping properties of the viscoelastic sandwich FGM beam are investigated successfully. It is shown that the beam behavior is very sensitive on the loss factor. In vibration, the damping properties are nonlinearly power law index dependent. The boundary conditions have an incidence on the vibration modes . The cantilever case is particular and interesting that needs an optimization process.
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Research context

OpenAlex topics: Composite Structure Analysis and Optimization · Railway Engineering and Dynamics · Vibration and Dynamic Analysis

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References (45)

Show source-provided references
1. C. Schneider-Maunoury, “ Application de l’injection différentielle au procédé de fabrication additive DED-CLAD® pour la réalisation d’alliages de titane à gradients de compositions chimiques, ” PhD thesis, Université de Lorraine, 2019.https://hal.univ-lorraine.fr/tel-02094994
2. FGM activities in Japan10.1016/S1359-8368(96)00016-9 ↗
3. Free vibration analysis of functionally graded beams with simply supported edges10.1016/j.matdes.2006.02.007 ↗
4. Dynamic response of antisymmetric cross-ply laminated composite beams with arbitrary boundary conditions10.1016/0020-7225(95)00080-1 ↗
5. Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression10.1016/j.ijmecsci.2017.01.011 ↗
6. Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories10.1016/j.nucengdes.2009.12.013 ↗
7. Free vibration of cross-ply laminated beams with arbitrary boundary conditions10.1016/0020-7225(94)90093-0 ↗
8. Effects of different shear deformation theories on free vibration of functionally graded beams10.1016/j.ijmecsci.2014.03.014 ↗
9. Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams10.1016/j.compstruc.2014.10.001 ↗
10. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories10.1016/j.ijmecsci.2012.05.014 ↗
11. A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams10.1016/j.compstruct.2019.04.002 ↗
12. T.K Nguyen, T. Truong-Phong Nguyen, T. P. Vo, and H.-T. Thai, “Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory,” Compos. Part B Eng., vol. 76, pp. 273–285, Jul. 2015, doi: 10.1016/j.compositesb.2015.02.032.10.1016/j.compositesb.2015.02.032 ↗
13. Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach10.1016/j.compstruct.2015.11.010 ↗
14. Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method10.1016/j.engstruct.2012.03.041 ↗
15. Free vibration analysis of sandwich beam with FG core using the element free Galerkin method10.1016/j.compstruct.2009.03.023 ↗
16. Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory10.1016/j.engstruct.2014.01.029 ↗
17. M. Filippi, E. Carrera, and AM. Zenkour, “Static analyses of FGM beams by various theories and finite elements,” Compos. Part B Eng. 72, (April 2015), 1–9. DOI:https://doi.org/10.1016/j.compositesb.2014.12.00410.1016/j.compositesb.2014.12.004 ↗
18. Analysis of FGM beams by means of classical and advanced theories10.1080/15376494.2010.518930 ↗
19. D.S. Mashat, E. Carrera, A.M. Zenkour, S.A.A.l. Khateeb, and M. Filippi, “Free vibration of FGM layered beams by various theories and finite elements,” Compos. Part B Eng. 59, 2014, 269–278. DOI:https://doi.org/10.1016/j.compositesb.2013.12.00810.1016/j.compositesb.2013.12.008 ↗
20. A. MilazzoandC. Orlando, “An equivalent single-layer approach for free vibration analysis of smart laminated thick composite plates,” Smart Materials and Structures, 21, 7. https://doi.org/10.1088/0964-1726/21/7/07503110.1088/0964-1726/21/7/075031 ↗
21. F. Tornabene, E. Viola and N. Fantuzzi, “General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels,” Composite Structures, 104, 2013, 94-117. doi.org/10.1016/j.compstruct.2013.04.00910.1016/j.compstruct.2013.04.009 ↗
22. An efficient layerwise finite element for shallow composite and sandwich shells10.1016/j.compstruct.2012.10.048 ↗
23. Review and assessment of various theories for modeling sandwich composites10.1016/j.compstruct.2007.08.007 ↗
24. M. W. Hyer, W. J. Anderson and R. A. Scott, “Non-linear vibrations of three-layer beams with viscoelastic core I. theory,” J. Sound Vib., (1976) 46(l), 121-136.doi.org/10.1016/0022-460X(76)90822-1.10.1016/0022-460X(76)90822-1 ↗
25. Non-linear vibrations of three-layer beams with viscoelastic cores, II: experiment10.1016/0022-460X(78)90038-X ↗
26. Forced non-linear vibrations of a damped sandwich beam10.1016/0022-460X(71)90131-3 ↗
27. Non-linear vibration analysis of multilayer beams by incremental finite elements, Part I: theory and numerical formulation10.1016/0022-460X(85)90292-5 ↗
28. A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures10.1016/S0045-7949(00)00151-6 ↗
29. Linear and nonlinear vibrations analysis of viscoelastic sandwich beams10.1016/j.jsv.2010.06.012 ↗
30. A generic approach for the solution of nonlinear residual equations. Part I: the Diamant toolbox10.1016/j.cma.2008.09.003 ↗
31. C. H. Bischof, H. M. Bücker, P. Hovland, U. Naumann and J. Utke, “Advances in automatic differentiation,” Springer-Verlag Heidelberg, 2006.
32. J. S. Moita, A. L. Araújo, C. M. Mota Soares, and C. A. Mota Soares, “Vibration analysis of functionally graded material sandwich structures with passive damping,” Compos. Struct., vol. 183, pp. 407–415, Jan. 2018, doi: 10.1016/j.compstruct.2017.04.045.10.1016/j.compstruct.2017.04.045 ↗
33. A modified Fourier-Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials10.1016/j.ijmecsci.2015.11.031 ↗
34. K. Koutoati, F. Mohri and E. M. Daya, “Finite element approach of axial bending coupling on static and vibration behaviors of functionally graded material sandwich beams,” Int. J. Mechanics of Advanced Materials and Structures. 2019 doi.org/10.1016/0022-460X(76)90822-1.10.1080/15376494.2019.1685144 ↗
35. A general non-linear third-order theory of plates with moderate thickness10.1016/0020-7462(90)90006-U ↗
36. An efficient standard plate theory10.1016/0020-7225(91)90165-Y ↗
37. M. Bilasse “Modélisation numérique des vibrations linéaires et non linéaires des structures sandwichs à âme viscoélastique,” PhD thesis, Université de Lorraine, 2010.https://hal.univ-lorraine.fr/tel-01748929
38. V. S. Rao, “Finite element analysis of viscoelastically damped composite structures,” PhD thesis, University of Florida. https://elibrary.ru/item.asp?id=5838935
39. C. Lanczos, “An iteration method for the solution of the eigenvalue problem of linear differential and integral operators,” United States Governm. Press Office Los Angeles, CA, 1950. http://www.cs.umd.edu/~oleary/lanczos1950.pdf10.6028/jres.045.026 ↗
40. Modeling of frequency-dependent viscoelastic materials for active-passive vibration damping10.1115/1.568429 ↗
41. M. Haberman, Design of high loss viscoelastic composites through micromechanical modeling and decision based material by design. Ph.D. Thesis, G. W. Woodruff School of Mechanical Engineering, Atlanta, 2007. http://hdl.handle.net/1853/14599
42. Méthode asymptotique numérique
43. A. Ed-dinari, H. Mottaqui, B. Braikat, M. Jamal, F. Mohri and N Damil, “Large torsion analysis of thin-walled open sections beams by the Asymptotic Numerical Method,” Engineering Structures 81 2014 240–255.10.1016/j.engstruct.2014.09.045 ↗
44. A Elkaimbillah, B Braikat, F Mohri, N Damil “A one-dimensional model for computing forced nonlinear vibration of thin-walled composite beams with open variable cross-sections”, Thin-Walled Structures, 2021, 159.Under Press.10.1016/j.tws.2020.107211 ↗
45. K. Koutoati “Modélisation numérique du comportement statique et vibratoire des poutres sandwich viscoélastiques à gradient de propriétés,” PhD thesis. Université de Lorraine, 2020.