Computers and Concrete

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Forced vibration analysis of a micro sandwich plate with an isotropic/orthotropic cores and polymeric nanocomposite face sheets

  • Rajabi, Javad (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.10.28
  • Accepted : 2021.08.13
  • Published : 2021.09.25
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Abstract

In this study, the forced vibration analysis of a micro sandwich plate with an isotropic/orthotropic cores and polymeric nanocomposite face sheets is taken into account based on first order shear deformation theory (FSDT). The core of this plate is considered as five isotropic Devineycell materials (H30, H45, H60, H100 and H200) and an orthotropic material, while facesheets layers are as polymeric matrix reinforced by carbon nanotubes under temperature-dependent and hydro material properties on the elastic foundations. The governing equations of motion are derived using the Hamilton's principle and then solved by analytical method. Also, the effects of different parameters such as size dependent, side ratio, volume fraction, various material properties of cores and facesheets and temperature and humidity changes on the dimensionless frequency are investigated. It is shown from the results that the dimensionless frequency for CT is lower than that of for MSGT. Also, it is presented that the least amplitude oscillation is related to the modified strain gradient theory due to higher stiffen. It is illustrated that the dimensionless frequency for Devineycell H200 is highest and lowest for H30. The results of this research can be used in aircraft, automotive, shipbuilding industries and biomedicine.

Keywords

Acknowledgement

The authors would like to thank the reviewers for their valuable comments and suggestions to improve the clarity of this work. Also, they be grateful the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work by Grant No. 891238/9.

References

  1. Ait, A.M.M., Abdelaziz, H.H. and Tounsi, A. (2014). "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16, 293-318. https://doi.org/10.1177/1099636214526852.
  2. Akbari Alashti, R. and Khorsand, M. (2012), "Tree-dimensional dynamo-thermo-elastic of a functionally graded cylindrical shell with piezoelectric layers by DQ-FD coupled", Int. J. Press. Ves. Pip., 96-97, 49-67. https://doi.org/10.1016/j.ijpvp.2012.06.006.
  3. Al-Osta, M.A. (2019), "Shear behaviour of RC beams retrofitted using UHPFRC panels epoxied to the sides", Comput. Concrete, 24(1), 37-49. https://doi.org/10.12989/cac.2019.24.1.037.
  4. Anitescu, C., Atroshchenko, F., Alajlan, N. and Rabczuk, T. (2019), "Artificial neural network methods for the solution of second order boundary value problems", Comput. Mater. Continua (CMC), 59(1), .345-359. https://doi.org/10.32604/cmc.2019.06641.
  5. Arani, A.G., Haghparast, E. and Zarei, H.B. (2017), "Vibration analysis of functionally graded nanocomposite plate moving in two directions", Steel Compos. Struct., 23(5), 529-541. https://doi.org/10.12989/scs.2017.23.5.529.
  6. Areias, P., Rabczuk, T. and Msekh, M. (2016), "Phase-field analysis of finite-strain plates and shells including element subdivision", Comput. Meth. Appl. Mech. Eng., 312(C), 322-350. https://doi.org/10.1016/j.cma.2016.01.020.
  7. Azizi, S., Safaei, B., Fattahi, AM. and Tekere, M. (2015), "Nonlinear vibrational analysis of nanobeams embedded in an elastic medium including surface stress effects", Adv. Mater. Sci. Eng., 2015, Article ID 318539. https://doi.org/10.1155/2015/318539.
  8. Bahaadini, R., Saidi, A.R. and Hosseini, M. (2019), "Flow-induced vibration and stability analysis of carbon nanotubes based on the nonlocal strain gradient Timoshenko beam theory", J. Vib. Control, 25(1), 203-218. https://doi.org/10.1177/1077546318774242.
  9. Boudjemai, A., Amri, R., Mankour, A., Salem, H., Bouanane, M.H. and Boutchicha, D. (2012), "Modal analysis and testing of hexagonal honeycomb plates used for satellite structural design", Mater. Des., 35, 266-275. https://doi.org/10.1016/j.matdes.2011.09.012.
  10. Brush, D.O. and Almroth, B.O. (1975), Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, NY, USA.
  11. Civalek, O. and Baltacioglu, A.K. (2019), "Free vibration analysis of laminated and FGM composite annular sector plates", Compos. Part B: Eng., 157, 182-194. https://doi.org/10.1016/j.compositesb.2018.08.101.
  12. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronaut, 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014.
  13. Ebrahimi, F., Nouraei, M., Dabbagh, A. and Civalek, O. (2019), "Buckling analysis of graphene oxide powder-reinforced nanocomposite beams subjected to non-uniform magnetic field", Struct. Eng. Mech., 71(4), 351-361. https://doi.org/10.12989/sem.2019.71.4.351.
  14. Elishakoff, I., Pentaras, D. and Gentilini, C. (2015), Mechanics of Functionally Graded Material Structures, World Scientific Publishing Co..
  15. Fan, Y., Xiang, Y. and Shen, H.S. (2019), "Nonlinear forced vibration of FG-GRC laminated plates resting on visco-Pasternak foundations", Compos. Struct., 209, 443-452. https://doi.org/10.1016/j.compstruct.2018.10.084.
  16. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. Part B: Eng., 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  17. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329, 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020.
  18. Gholami, R. and Ansari, R. (2018), "Nonlinear stability and vibration of pre/post buckled multilayer FG-GPLRPC rectangular plates", Appl. Math. Model., 65, 627-660. https://doi.org/10.1016/j.apm.2018.08.038.
  19. Ghorbanpour Arani, A., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016), "Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory", Compos. Part B: Eng., 95, 209-224. https://doi.org/10.1016/j.compositesb.2016.03.077.
  20. Hamdia, K.M., Silani, M., Zhuang, X., He, P. and Rabczuk, T. (2017), "Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions", Int. J. Fract., 206(2), 215-227. https://doi.org/10.1007/s10704-017-0210-6.
  21. Hosseini-Hashemi, S., Arpanahi, R.A., Rahmanian, S. and Ahmadi-Savadkoohi, A. (2019), "Free vibration analysis of nano-plate in viscous fluid medium using nonlocal elasticity", Europ. J. Mech./A Solid., 74, 440-448. https://doi.org/10.1016/j.euromechsol.2019.01.002.
  22. Ji, L., Mace, B.R. and Pinnington, RJ. (2004), "A hybrid mode/Fourier-transform approach for estimating the vibrations of beam-stiffened plate systems", J Sound Vib., 274, 547-565. https://doi.org/10.1016/j.jsv.2003.06.028.
  23. Karimiasl, M., Ebrahimi, F. and Mahesh, V. (2019), "Nonlinear forced vibration of smart multiscale sandwich composite doublycurved porous shell", Thin Wall. Struct., 143, 106-152. https://doi.org/10.1016/j.tws.2019.04.044.
  24. Kolahdouzan, F., Arani, A.G. and Abdollahian, M. (2018), "Buckling and free vibration analysis of FG-CNTRC-micro sandwich plate", Steel Compos. Struct., 26(3), 273-287. https://doi.org/10.12989/scs.2018.26.3.273.
  25. Kraus, H. (1967), Thin Elastic Shells, Wiley, New York, NY, USA.
  26. Lei, Z., Liew, K. and Yu, J. (2013), "Free vibration analysis of functionally graded carbon nanotubereinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138. https://doi.org/10.1016/j.compstruct.2013.06.003.
  27. Leissa, AW. (1993), Vibration of Shells, US Government Printing Office Reprinted by the Acoustical Society of America, Washington DC, USA.
  28. Liew, K.M., Zhao, X. and Ferreira, A.J.M. (2011), "A review of meshless methods for laminated and functionally graded plates and shells", Compos. Struct., 93, 2031-2041. https://doi.org/10.1016/j.compstruct.2011.02.018.
  29. Lin, F. and Xiang, Y. (2014), "Numerical analysis on nonlinear free vibration of carbon nanotube reinforced composite beams", Int. J. Struct. Stab. Dyn., 14(1), 1350056. https://doi.org/10.1142/S0219455413500569.
  30. Liu, S., Yu, T., Lich, L.V., Yin, S. and Bui, T.Q. (2018), "Size effect on cracked functional composite micro-plates by an XIGA-based effective approach", Meccanica, 53, 2637-2658. https://doi.org/10.1007/s11012-018-0848-9.
  31. Liu, S., Yu, T., Lich, L.V., Yin, S. and Bui, T.Q. (2019), "Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis", Comput. Struct., 212, 173-187. https://doi.org/10.1016/j.compstruc.2018.10.009.
  32. Lou, J., Ma, L. and Wu, L.Z. (2012), "Free vibration analysis of simply supported sandwich beams with lattice truss core", Mater. Sci. Eng. B., 177, 1712-1716. https://doi.org/10.1016/j.mseb.2012.02.003.
  33. Lou, J., Wu, L.Z., Ma, L., Xiong, J. and Wang, B. (2014), "Effects of local damage on vibration characteristics of composite pyramidal truss core sandwich structure", Compos. Part B: Eng., 62, 73-87. https://doi.org/10.1016/j.compositesb.2014.02.012.
  34. Meksi, R., Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2017), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  35. Mohammadimehr, M. and Mostafavifar, M. (2016), "Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT", Compos. Part B, 94, 253-270. https://doi.org/10.1016/j.compositesb.2016.03.030.
  36. Mohammadimehr, M. and Rostami, R. (2017), "bending, buckling, and forced vibration analyses of nonlocal nanocomposite microplate using tsdt considering mee properties dependent to various volume fractions of cofe2o4-batio3", J. Theor. Appl. Mech., 55(3), 853-868. https://doi.org/10.15632/jtampl.55.3.853.
  37. Mohammadimehr, M. and Shahedi, S. (2016), "Nonlinear magneto-electro-mechanical vibration analysis of doublebonded sandwich Timoshenko microbeams based on MSGT using GDQM", Steel Compos. Struct., 21(1), 1-36. https://doi.org/10.12989/scs.2016.21.1.001.
  38. Mohammadimehr, M., Mehrabi, M., Hadizadeh, H., Hadizadeh, H. (2018b), "Surface and size dependent effects on static, buckling, and vibration of micro composite beam under thermo-magnetic fields based on strain gradient theory", Steel Compos. Struct., 26(4), 513-531. https://doi.org/10.12989/scs.2018.26.4.513.
  39. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2016), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B, 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007.
  40. Mohammadimehr, M., Rousta Navi, B., Ghorbanpour Arani, A., Navi, B.R. and Ghorbanpour Arani, A. (2016), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B: Eng., 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007.
  41. Mohammadimehr, M., Shabani Nejad, E. and Mehrabi, M. (2018c), "Buckling and vibration analyses of MGSGT double-bonded micro composite sandwich SSDT plates reinforced by CNTs and BNNTs with isotropic foam & flexible transversely orthotropic cores", Struct. Eng. Mech., 65(4), 491-504. https://doi.org/10.12989/sem.2018.65.4.491.
  42. Mohammadimehr, M., Zarei, H.B., Parakandeh, A. and Arani, A.G. (2017), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., 64(3), 361-379. https://doi.org/10.12989/sem.2017.64.3.361.
  43. Mohammadsalehi, M., Zargar, O. and Baghani, M. (2017), "Study of non-uniform viscoelastic nanoplates vibration based on nonlocal first-order shear deformation theory", Meccanica, 52, 1063-1077. https://doi.org/10.1007/s11012-016-0432-0.
  44. Msekh, M.A., Cuong, N.H., Zi, G., Areias, P., Zhuang, X. and Rabczuk, T. (2018), "Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model", Eng. Fract. Mech., 188, 287-299. https://doi.org/10.1016/j.engfracmech.2017.08.002.
  45. Nguyen, L., Hoang, C., Zenkour, A.M. and Nguyen-Xuan, H. (2019), "An isogeometric Bezier fnite element method for vibration analysis of functionally graded piezoelectric material porous plates", Int. J. Mech. Sci., 157-158, 165-183 . https://doi.org/10.1016/j.ijmecsci.2019.04.017.
  46. Nguyen-Thanh, N., Zhou, K., Zhuang, X., Areias, P., Bazilevs, Y. and Rabczuk, T. (2017), "Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling", Comput. Meth. Appl. Mech. Eng., 316, 1157-1178. https://doi.org/10.1016/j.cma.2016.12.002.
  47. Qatu, M. (2004), Vibration of Laminated Shells and Plates, First Edition, Academic Press, USA.
  48. Rabczuk, T., Ren, H. and Zhuang, X. (2019), "A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem", Comput. Mater. Continua (CMC), 59(1),.31-55. https://doi.org/10.32604/cmc.2019.04567.
  49. Ramu, I. and Mohanty, S.C. (2012), "Study on free vibration analysis of rectangular plate structures using finite element method", Procedia Eng., 38, 2758-2766. https://doi.org/10.1016/j.proeng.2012.06.323.
  50. Reddy, J.N. (2003), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Second Edition, CRC Press, New York, NY, USA.
  51. Safaei, B., Moradi-Dastjerdi, R., Behdinan, K. and Chu, F. (2019), "Critical buckling temperature and force in porous sandwich plates with CNT-reinforced nanocomposite layers", Aerosp. Sci. Technol., 91, 175-185. https://doi.org/10.1016/j.ast.2019.05.020.
  52. Safaei, B., Moradi-Dastjerdi, R., Qin, Z. and Chu, F. (2018), "Frequency-dependent forced vibration analysis of nanocomposite sandwich plate under thermo-mechanical loads", Compos. Part B, 161, 44-54. https://doi.org/10.1016/j.compositesb.2018.10.049.
  53. Shen, H.S. (2009), Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, CRC Press, New York, NY, USA.
  54. Shen, H.S. (2011), "Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part I: Axially-loaded shells", Compos. Struct., 93, 2096-2108. https://doi.org/10.1016/j.compstruct.2011.02.011.
  55. Shen, H.S. and Xiang, Y. (2015), "Nonlinear response of nanotube-reinforced composite cylindrical panels subjected to combined loadings and resting on elastic foundations", Compos. Struct., 131, 939-950. https://doi.org/10.1016/j.compstruct.2015.06.042.
  56. Shen, H.S. and Xiang, Y. (2015), "Thermal postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations", Compos. Struct., 123, 383-392. https://doi.org/10.1016/j.compstruct.2014.12.059.
  57. Shen, H.S., Wang, H. and Yang, D.Q. (2017), "Vibration of thermally postbuckled sandwich plates with nanotube-reinforced composite face sheets resting on elastic foundations", Int. J. Mech. Sci., 124, 253-262. https://doi.org/10.1016/j.ijmecsci.2017.03.015.
  58. Shen, M., Shi, Z., Zhao, C., Zhong, X., Liu, B. and Shu, X. (2019), "2-D meso-scale complex fracture modeling of concrete with embedded cohesive elements", Comput Concrete, 24(3), 207-222. https://doi.org/10.12989/cac.2019.24.3.207.
  59. Soedel, W. (2004), Vibrations of Shells and Plates, Third Edition, CRC Press, New York, NY, USA.
  60. Syiemiong, H. and Marthong, C. (2019), "Effect of moisture on the compressive strength of low-strength hollow concrete blocks", Comput Concrete, 23(4), 267-272. https://doi.org/10.12989/cac.2019.23.4.267.
  61. Talebi, H., Silani, M., Bordas, S.P.A., Rabczuk, T. and Kerfriden, P. (2014), "A computational library for multiscale modeling of material failure", Comput. Mech., 53, 1047-1071. https://doi.org/10.1007/s00466-013-0948-2.
  62. Tang, C.W. (2019), "Residual properties of high-strength fiber reinforced concrete after exposure to high temperatures", Comput Concrete, 24(1), 63-71. http://doi.org/10.12989/cac.2019.24.1.063.
  63. Tornabene, F. (2009), "Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2911-2935. https://doi.org/10.1016/j.cma.2009.04.011.
  64. Tornabene, F. and Fantuzzi, N. (2014), Mechanics of Laminated Composite Doubly-Curved Shell Structures, Societa Editrice Esculapio, Italy.
  65. Tornabene, F., Liverani, A. and Caligiana, G. (2011), "FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: A 2-D GDQ solution for free vibrations", Int. J. Mech. Sci., 53(6), 446-470. https://doi.org/10.1016/j.ijmecsci.2011.03.007.
  66. Vu, T.V., Khosravifard, A., Hematiyan, M.R. and Bui, T.Q. (2018), "A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates", Appl. Math. Model., 57, 514-534. https://doi.org/10.1016/j.ijmecsci.2011.03.007.
  67. Vu, T.V., Nguyen, N.H., Khosravifard, A., Hematiyan, M.R., Tanaka, S. and Bui, T.Q. (2017), "A simple FSDT-based meshfree method for analysis of functionally graded plates", Eng. Anal. Bound. Elem., 79, 1-12. https://doi.org/10.1016/j.enganabound.2017.03.002.
  68. Vu-Bac, N., Lahmer, T., Zhuang, X., Nguyen-Thoi, T. and Rabczuk, T. (2016), "A software framework for probabilistic sensitivity analysis for computationally expensive models", Adv. Eng. Softw., 100, 19-31. https://doi.org/10.1016/j.advengsoft.2016.06.005.
  69. Wang, J., Chen, X., Bu, X. and Guo, S. (2019), "Experimental and numerical simulation study on fracture properties of self-compacting rubberized concrete slabs", Comput. Concrete, 24(4), 283-293. https://doi.org/10.12989/cac.2019.24.4.283.
  70. Wang, X., Han, B., Zhao, Z.Y., Li, L., Zhang, Z.J., Zhang, Q.C. and Lu, T.J. (2019), "Free vibration behavior of Ti-6Al-4V sandwich beams with corrugated channel cores: Experiments and simulations", Thin Wall. Struct., 135, 329-340. https://doi.org/10.1016/j.tws.2018.11.008.
  71. Yin, S., Hale, J.S., Yu, T., Bui, T.Q. and Bordas, S.P.A. (2014), "Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates", Compos. Struct., 118, 121-138. https://doi.org/10.1016/j.compstruct.2014.07.028.
  72. Yu, T., Yin, S., Bui, T.Q., Xia, S., Tanaka, S. and Hirose, S. (2016), "NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method", Thin Wall. Struct., 101, 141-156. https://doi.org/10.1016/j.tws.2015.12.008.
  73. Yu, T.T., Yin, S., Bui, T.Q. and Hirose, S. (2015), "A simple FSDT-based isogeometric analysis for geometrically nonlinear analysis of functionally graded plates", Finite Elem. Anal. Des., 96, 1-10. https://doi.org/10.1016/j.finel.2014.11.003.
  74. Zenkour, AM. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part1 deflection and stresses", Int. J. Solid. Struct., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  75. Zenkour, AM. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2 buckling and free vibration", Int. J. Solid. Struct., 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  76. Zghal, S. and Nasri, R. (2017), "Experimental investigation for forced vibration of honeycomb sandwich beams", Adv. Acoust. Vib., 5, 223-233. https://doi.org/10.1007/978-3-319-41459-1_22.
  77. Zhang, H., Rupeng, Zh., Dongyan, Sh. and Qingshan, W. (2019), "A simplified plate theory for vibration analysis of composite laminated sector, annular and circular plate", Thin Wall. Struct., 143, 106252. https://doi.org/10.1016/j.tws.2019.106252.
  78. Zhang, K. and Tian, R.L. (2019), "An analytical study of vibration response of a beam stiffened Mindlin plate", Appl. Acoust., 155, 32-43. https://doi.org/10.1016/j.apacoust.2019.05.004.
  79. Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R. and Shuai, C. (2019), "Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions", Compos. Part B., 168, 106-120. https://doi.org/10.1016/j.compositesb.2018.12.044.
  80. Zhenkun, G., Chunchuan, L. and Fengming, L. (2017), "Vibration analysis of sandwich plates with lattice truss core", Mech. Adv. Mater. Struct., 26, 424-429. https://doi.org/10.1080/15376494.2017.1400616.