DOI QR코드

DOI QR Code

Vibration analysis of sandwich beam with nanocomposite facesheets considering structural damping effects

  • Cheraghbak, Ali (Faculty of Engineering, Shahrekourd University) ;
  • Dehkordi, M. Botshekanan (Faculty of Engineering, Shahrekourd University) ;
  • Golestanian, H. (Faculty of Engineering, Shahrekourd University)
  • 투고 : 2019.05.05
  • 심사 : 2019.08.27
  • 발행 : 2019.09.25

초록

In this paper, free vibration of sandwich beam with flexible core resting on orthotropic Pasternak is investigated. The top and bottom layers are reinforced by carbon nanotubes (CNTs). This sandwich structural is modeled by Euler and Frostig theories. The effect of agglomeration using Mori-Tanaka model is considered. The Eringen's theory is applied for size effect. The structural damping is investigated by Kelvin-voigt model. The motion equations are calculated by Hamilton's principle and energy method. Using analytical method, the frequency of the structure is obtained. The effect of agglomeration and CNTs volume percent for different parameter such as damping of structure, thickens and spring constant of elastic medium are presented on the frequency of the composite structure. Results show that with increasing CNTs agglomeration, frequency is decreased.

키워드

참고문헌

  1. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higherorder shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  2. Chan, D.Q., Anh, V.T.T. and Duc, N.D. (2018), "Vibration and nonlinear dynamic response of eccentrically stiffened functionally graded composite truncated conical shells in thermal environments", Acta Mech., 230, 157-178. https://doi.org/10.1007/s00707-018-2282-4
  3. Chung, D.N., Dinh, N.N., Hui, D., Duc, N.D., Trung, T.Q. and Chipara, M. (2013), "Investigation of Polymeric Composite Films Using Modified TiO2 Nanoparticles for Organic Light Emitting Diodes", J. Current Nanosci., 9, 14-20. https://doi.org/10.2174/157341313805118018
  4. Duc, N.D. (2014a), Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press, Hanoi, Vietnam.
  5. Duc, N.D. (2014b), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", J. Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017
  6. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech. - A/Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004
  7. Duc, N.D. and Minh, D.K. (2010), "Bending analysis of threephase polymer composite plates reinforced by glass fibers and Titanium oxide particles", J. Computat. Mat. Sci., 49, 194-198. https://doi.org/10.1016/j.commatsci.2010.04.016
  8. Duc, N.D., Quan, T.Q. and Nam, D. (2013), "Nonlinear stability analysis of imperfect three phase polymer composite plates", J. Mech. Compos. Mater., 49, 345-358. https://doi.org/10.1007/s11029-013-9352-4
  9. Duc, N.D., Hadavinia, H., Thu, P.V. and Quan, T.Q. (2015), "Vibration and nonlinear dynamic response of imperfect threephase polymer nanocomposite panel resting on elastic foundations under hydrodynamic loads", Compos. Struct., 131, 229-237. https://doi.org/10.1016/j.compstruct.2015.05.009
  10. Duc, N.D., Khoa, N.D. and Thiem, H.T. (2018), "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy's third-order shear deformation shell theory", Mech. Adv. Mater. Struct., 25, 1157-1167. https://doi.org/10.1080/15376494.2017.1341581
  11. Dutta, G., Panda. S.K., Mahapatra, T.R. and Singh, V.K. (2017), "Electro-magneto-elastic response of laminated composite plate: A finite element approach", Int. J. Appl. Computat. Math., 3, 2573-2592. https://doi.org/10.1007/s40819-016-0256-6
  12. Daya, E.M., Azrar, L. and Potier-Ferry, M. (2004), "An amplitude equation for the non-linear vibration of viscoelastically damped sandwich beams", J. Sound Vib., 271, 789-813. https://doi.org/10.1016/S0022-460X(03)00754-5
  13. Eltaher, M.A., El-Borgi, S. and Reddy, J.N. (2016), "Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs", Compos. Struct., 153, 902-913. https://doi.org/10.1016/j.compstruct.2016.07.013
  14. Frostig, Y. (2003), "An efficient higher order zigzag theory for composite and sandwich beams subjected to thermal loading", Int. J. Solids Struct., 40, 6613-6631. https://doi.org/10.1016/j.ijsolstr.2003.08.014
  15. Garcia-Maciasa, E. and Castro-Triguero, R. (2018), "Coupled effect of CNT waviness and agglomeration: A case study of vibrational analysis of CNT/polymer skew plates", Compos. Struct., 193, 87-102. https://doi.org/10.1016/j.compstruct.2018.03.001
  16. Kapuria, S., Ahmed, A. and Dumir, P.C. (2005), "An efficient coupled zigzag theory for dynamic analysis of piezoelectric composite and sandwich beams with damping", J. Sound Vib., 279, 345-371. https://doi.org/10.1016/j.jsv.2003.11.018
  17. Khalili, S.M.R., Botshekanan Dehkordi, M., Carrera, E. and Shariyat, M. (2013), "Non-linear dynamic analysis of a sandwich beam with pseudoelastic SMA hybrid composite faces based on higher order finite element theory", Compos. Struct., 96, 243-255. https://doi.org/10.1016/j.compstruct.2012.08.020
  18. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016
  19. Kutlu, A., Ugurlu, B., Omurtag, M.H. and Ergin, A. (2012), "Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid", Ocean Eng., 42, 112-125. https://doi.org/10.1016/j.oceaneng.2012.01.010
  20. Lakreb, N., Bezzazi, B. and Pereira, H. (2015), "Mechanical behavior of multilayered sandwich panels of wood veneer and a core of cork agglomerates", Mater. Des., 65, 627-636. https://doi.org/10.1016/j.matdes.2014.09.059
  21. Li, Z., Chu, J., Yang, C., Hao, S., Bissett, M.A., Kinloch, I.A. and Young, R.J. (2018), "Effect of functional groups on the agglomeration of graphene in Nano composites", Compos. Sci. Technol., 163, 116-122. https://doi.org/10.1016/j.compscitech.2018.05.016
  22. Lim, J.Y. and Bart-Smith, H. (2015), "An analytical model for the face wrinkling failure prediction of metallic corrugated core sandwich columns in dynamic compression", Int. J. Mech. Sci., 92, 290-303. https://doi.org/10.1016/j.ijmecsci.2015.01.002
  23. Liu, Y., Yu, K., Hu, H., Belouettar, S., Potier-Ferry, M. and Damil, N. (2012), "A new Fourier-related double scale analysis for instability phenomena in sandwich structures", Int. J. Solids Struct., 49, 3077-3088. https://doi.org/10.1080/15376494.2015.1085606
  24. Loghman, A. and Cheraghbak, A. (2016), "Agglomeration Effects on Electro-magnetothermo Elastic Behavior of Nano-composite Piezoelectric Cylinder", Polym. Compos., 39(5), 1594-1603. https://doi.org/10.1002/pc.24104
  25. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNTreinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., Int. J., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  26. Mahapatra, T.R. and Panda, S.K. (2016), "Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal environment: A micromechanical approach", Aerosp. Sci. Technol., 49, 276-288. https://doi.org/10.1016/j.ast.2015.12.018
  27. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016a), "Nonlinear flexural analysis of laminated composite panel under hygrothermo- mechanical loading-A micromechanical approach", Int. J. Computat. Meth., 13, 1650015. https://doi.org/10.1142/S0219876216500158
  28. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model", Mech. Advan. Mater. Struct., 23, 1343-1359. https://doi.org/10.1080/15376494.2015.1085606
  29. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016c), "Geometrically nonlinear flexural analysis of hygro-thermoelastic laminated composite doubly curved shell panel", Int. J. Mech. Mat. Des., 12, 153-171. https://doi.org/10.1007/s10999-015-9299-9
  30. Mahi, A., Bedia, E.A.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  31. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech. A/Solids 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005
  32. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall. Mater., 21, 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  33. Nejati, M., Asanjarani, A., Dimitri, R. and Tornabene, F. (2017), "Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes", Int. J. Mech. Sci., 130, 383-398. https://doi.org/10.1016/j.ijmecsci.2017.06.024
  34. Qin, Q.H. and Wang, T.J. (2009), "A theoretical analysis of the dynamic response of metallic sandwich Beam under impulsive loading", Eur. J. Mech. A/Solids, 28, 1014-1025. https://doi.org/10.1016/j.euromechsol.2009.04.002
  35. Quan, T.Q., Tran, P., Tuan, N.D. and Duc, N.D. (2015), "Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metal-ceramic-metal layers resting on elastic foundations", Compos. Struct., 126, 16-33. https://doi.org/10.1016/j.compstruct.2015.02.056
  36. Safaeia, B., Moradi-Dastjerdib, R. and Chu, F. (2018), "Effect of thermal gradient load on thermo-elastic vibrational behavior of sandwich plates reinforced by carbon nanotube agglomerations", Compos. Struct., 192, 28-37. https://doi.org/10.1016/j.compstruct.2018.02.022
  37. Shokravi, M. (2018), "Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory", Steel Compos. Struct., Int. J., 28(3), 381-388. https://doi.org/10.12989/scs.2018.28.3.381
  38. Smyczynski, M.J. and Magnucka-Blandzi, E. (2018), "Stability of five layer sandwich beams - a nonlinear hypothesis", Steel Compos. Struct., Int. J., 28(6), 671-679. https://doi.org/10.12989/scs.2018.28.6.671
  39. Sorokin, S.V. and Grishina, S.V. (2004), "Analysis of wave propagation in sandwich beams with parametric stiffness modulations", J. Sound Vib., 271, 1063-1082. https://doi.org/10.1016/j.jsv.2003.03.005
  40. Suman, S.D., Hirwani, C.K., Chaturvedi, A. and Panda, S.K. (2017), "Effect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure", IOP Conference Series: Materials Science and Engineering, 178(1), 012026. https://doi.org/10.1088/1757-899X/178/1/012026
  41. Thu, P.V. and Duc, N.D. (2016), "Nonlinear dynamic response and vibration of an imperfect three-phase laminated nanocomposite cylindrical panel resting on elastic foundations in thermal environments", J. Sci. Eng. Compos. Mater., 24(6), 951-962. https://doi.org/10.1515/secm-2015-0467
  42. Vuong, P.M. and Duc, N.D. (2018), "Nonlinear response and buckling analysis of eccentrically stiffened FGM toroidal shell segments in thermal environment", Aerosp. Sci. Technol., 79, 383-398. https://doi.org/10.1016/j.ast.2018.05.058
  43. Zeinedini, A., Shokrieh, M.M. and Ebrahimi, A. (2018), "The effect of agglomeration on the fracture toughness of CNTsreinforced Nano composites", Theoret. Appl. Fract. Mech., 94, 84-94. https://doi.org/10.1016/j.tafmec.2018.01.009

피인용 문헌

  1. Evaluation of equivalent friction damping ratios at bearings of welded large-scale domes subjected to earthquakes vol.40, pp.4, 2021, https://doi.org/10.12989/scs.2021.40.4.517