DOI QR코드

DOI QR Code

Free vibration analysis of angle-ply laminated composite and soft core sandwich plates

  • Sahla, Meriem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Saidi, Hayat (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Draiche, Kada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2019.05.08
  • Accepted : 2019.11.19
  • Published : 2019.12.10

Abstract

In this work, a simple four-variable trigonometric shear deformation model with undetermined integral terms to consider the influences of transverse shear deformation is applied for the dynamic analysis of anti-symmetric laminated composite and soft core sandwich plates. Unlike the existing higher order theories, the current one contains only four unknowns. The equations of motion are obtained using the principle of virtual work. The analytical solution is determined by solving the eigenvalue problem. The influences of geometric ratio, modular ratio and fibre angle are critically evaluated for different problems of laminated composite and sandwich plates. The eigenfrequencies obtained using the current theory are verified by comparing the results with those of other theories and with the exact elasticity solution, if any.

Keywords

References

  1. Aagaah, M.R., Mahinfalah, M. and Jazar, G.N. (2006), "Natural frequencies of laminated composite plates using third order shear deformation theory", Compos. Struct., 72, 273-279. https://doi.org/10.1016/j.compstruct.2004.11.012
  2. Afsharmanesh, B., Ghaheri, A. and Taheri-Behrooz, F. (2014), "Buckling and vibration of laminated composite circular plate on Winkler-type foundation", Steel Compos. Struct., Int. J., 17(1), 1-19. https://doi.org/10.12989/scs.2014.17.1.001
  3. Akbas, S.D. (2016), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  4. Akbas, S.D. (2018), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., Int. J., 67(4), 337-346. https://doi.org/10.12989/sem.2018.67.4.337
  5. Ashour, A.S. (2003), "Buckling and vibration of symmetric laminated composite plates with edges elastically restrained", Steel Compos. Struct., Int. J., 3(6), 439-450. https://doi.org/10.12989/scs.2003.3.6.439
  6. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., Int. J., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871
  7. Avcar, M. (2016), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A, 130(1), 375-378. https://doi.org/10.12693/APhysPolA.130.375.
  8. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  9. Baltacioglu, A.K. and Civalek, O. (2018), "Numerical approaches for vibration response of annular and circular composite plates", Steel Compos. Struct., Int. J., 29(6), 755-766. https://doi.org/10.12989/scs.2018.29.6.759.
  10. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018) "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., Int. J., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761
  11. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., Int. J., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517
  12. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  13. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339
  14. Bert, C.W. and Chen, T.L.C. (1978), "Effect of shear deformation on vibration of antisymmetric angle ply laminated rectangular plates", Int. J. Solids Struct., 14, 465-473. https://doi.org/10.1016/0020-7683(78)90011-2
  15. Brischetto, S. (2014), "An exact 3d solution for free vibrations of multilayered cross-ply composite and sandwich plates and shells", Int. J. Appl. Mech., 6, 1-42. https://doi.org/10.1142/S1758825114500768
  16. Carrera, E. (1999), "A study of transverse normal stress effect on vibration of multilayered plates and shells", J. Sound Vib., 225, 803-829. https://doi.org/10.1006/jsvi.1999.2271
  17. Chakrabarti, A. and Sheikh, A.H. (2004), "Vibration of laminate-faced sandwich plate by a new refined element", ASCE J. Aerosp. Eng., 17, 123-134. https://doi.org/10.1061/(ASCE)08931321(2004)17:3(123)
  18. Chalak, H.D., Chakrabarti, A., Iqbal, M. and Sheikh, A.H. (2013), "Free vibration analysis of laminated soft core sandwich plates", J. Vib. Acoust., 135, 1-15. https://doi.org/10.1115/1.4007262
  19. Chandra Mouli, B., Ramji, K., Kar, V.R., Panda, S.K., Lalepalli, A.K. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., Int. J., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527
  20. Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A.A. (2018), "Critical buckling load of chiral double-walled carbon nanotubes embedded in an elastic medium", Mech. Compos. Mater., 53(6), 827-836. https://doi.org/10.1007/s11029-018-9708-x
  21. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  22. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  23. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  24. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Computat., 229, 283-229. https://doi.org/10.1016/j.amc.2013.12.072
  25. Fadoun, O.O., Borokinni, A.S., Layeni, O.P. and Akinola, A.P. (2017), "Dynamics analysis of a transversely isotropic nonclassical thin plate", Wind Struct., Int. J., 25(1), 25-38. https://doi.org/10.12989/was.2017.25.1.025
  26. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007
  27. Ghugal, Y.M. and Pawar, M.D. (2011), "Buckling and vibration of plates by hyperbolic shear deformation theory", J. Aerosp. Eng. Technol., 1, 1-12.
  28. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Dynamic behavior of FGM beam using a new first shear deformation theory", Earthq. Struct., Int. J., 10(2), 451-461. https://doi.org/10.12989/eas.2016.10.2.451
  29. Javed, S., Viswanathan, K.K., Izyan, M.N., Aziz, Z.A. and Lee, J.H. (2018), "Free vibration of cross-ply laminated plates based on higher-order shear deformation theory", Steel Compos. Struct., Int. J., 26(4), 473-484. https://doi.org/10.12989/scs.2018.26.4.473
  30. Kant, T. and Manjunatha, BS. (1988), "An un-symmetric FRC laminate C3 finite element model with 12 degrees of freedom per node", Eng. Comput., 5, 300-308. https://doi.org/10.1108/eb023749
  31. Kant, T. and Swaminathan, K. (2001a), "Analytical solution for free vibration analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 53, 73-85. https://doi.org/10.1016/S0263-8223(00)00180-X
  32. Kant, T. and Swaminathan, K. (2001b), "Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories", J. Sound Vib., 241, 319-327. https://doi.org/10.1006/jsvi.2000.3232
  33. Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  34. Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solids Struct., 12(11), 2006-2024. http://dx.doi.org/10.1590/1679-78251691
  35. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronaut., 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007
  36. Kar, V.R. and Panda, S.K. (2017), "Large-amplitude vibration of functionally graded doubly-curved panels under heat conduction", AIAA J., 55(12), 4376-4386. https://doi.org/10.2514/1.J055878
  37. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proc. IMechE, Part L: J Materials: Design and Applications, 223, 53-62. https://doi.org/10.1243/14644207JMDA189
  38. Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., Int. J., 7(1), 51-61. https://doi.org/10.12989/anr.2019.7.1.051
  39. 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
  40. Kulkarni, S.D. and Kapuria, S. (2008), "Free vibration analysis of composite and sandwich plates using an improved discrete Kirchhoff quadrilateral element based on third order zigzag theory", Comput. Mech., 42, 803-824. https://doi.org/10.1007/s00466-008-0285-z
  41. Kumar, P. and Srinivas, J. (2018), "Transient vibration analysis of FG-MWCNT reinforced composite plate resting on foundation", Steel Compos. Struct., Int. J., 29(5), 569-578. https://doi.org/10.12989/scs.2018.29.5.569
  42. Liu, Q. and Zhao, Y. (2007), "Effect of soft honeycomb core on flexural vibration of sandwich panel using low order and high order shear deformation models", J. Sandw. Struct. Mater., 9, 95-108. https://doi.org/10.1177/1099636207070588
  43. Matsunaga, H. (2001), "Vibration and stability of angle ply laminated composite plates subjected to in-plane stresses", Int. J. Mech. Sci., 43, 1925-1944. https://doi.org/10.1016/S0020-7403(01)00002-9
  44. Mehar, K., Panda, S.K., Dehengia, A. and Kar, V.R. (2016), "Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment", J. Sandw. Struct. Mater., 18(2), 151-173. https://doi.org/10.1177/1099636215613324
  45. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38. https://doi.org/10.1115/1.4010217
  46. Naserian-Nik, A.M. and Tahani, M. (2010), "Free vibration analysis of moderately thick rectangular laminated composite plates with arbitrary boundary conditions", Struct. Eng. Mech., Int. J., 35(2), 217-240. https://doi.org/10.12989/sem.2010.35.2.217
  47. Noor, A.K. and Burton, W.S. (1989), "Free vibration of multilayered composite plates", Compos. Struct., 11, 183-204. https://doi.org/10.2514/3.6868
  48. Noor, A.K. and Burton, W.S. (1990), "Three-dimensional solutions for anti-symmetrically laminated anisotropic plates", ASME J. Appl. Mech., 57, 182-188. https://doi.org/10.1115/1.2888300
  49. Pandya, B.N. and Kant, T. (1988), "Finite element stress analysis of laminated composite plates using higher-order displacement model", Compos. Sci. Technol., 32, 137-155. https://doi.org/10.1016/0266-3538(88)90003-6
  50. Panjehpour, M., Loh, E. and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architect., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  51. Rao, M.K. and Desai, Y.M. (2004), "Analytical solutions for vibrations of laminated and sandwich plates using mixed theory", Compos. Struct., 63, 361-373. https://doi.org/10.1016/S0263-8223(03)00185-5
  52. Rao, M.K., Scherbatiuk, K., Desai, Y.M. and Shah, A.H. (2004), "Natural vibrations of laminated and sandwich plates", ASCE J. Eng. Mech., 130, 1268-1278. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:11(1268)
  53. Reddy, J.N. (1979), "Free vibration of antisymmetric angle ply laminated plates including transverse shear deformation by the finite element method", J. Sound Vib., 4, 565-576. https://doi.org/10.1016/0022-460X(79)90700-4
  54. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", ASME J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  55. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans ASME, 12(2), 69-77. https://doi.org/10.1016/0020-7683(76)90001-9
  56. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.4.329
  57. Sahouane, A., Hadji, L. and Bourada, M. (2019), " Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., Int. J., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031
  58. Sayyad, A.S. and Ghugal, Y.M. (2015), "On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007
  59. Sayyad, A.S. and Ghugal, Y.M. (2017), "On the free vibration of angle-ply laminated composite and soft core sandwich plates", J. Sandw. Struct. Mater., 19(6), 679-711. https://doi.org/10.1177/1099636216639000
  60. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445
  61. Senthilnathan, N.R., Lim, S.P., Lee, K.H. and Chow, S.T. (1988), "Vibration of laminated orthotropic plates using a simplified higher order deformation theory", Compos. Struct., 10, 211-229. https://doi.org/10.1016/0263-8223(88)90020-7
  62. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40. https://doi.org/10.12691/ajn-6-1-4
  63. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94, 195-200. https://doi.org/10.1007/bf01176650
  64. Thai, H.T. and Kim, S.E. (2010), "Free vibration of laminated composite plates using two variable refined plate theory", Int. J. Mech. Sci., 52, 626-633. https://doi.org/10.1016/j.ijmecsci.2010.01.002
  65. Whitney, J.M. (1969), "The effect of transverse shear deformation on the bending of laminated plates", J. Compos. Mater., 3, 534- 547. https://doi.org/10.1177/002199836900300316
  66. Yan, P.C., Norris, C.H. and Stavsky, Y. (1966), "Elastic wave propagation in heterogeneous plates", Int. J. Solids Struct., 2, 665-684. https://doi.org/10.1016/0020-7683(66)90045-X

Cited by

  1. Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection vol.9, pp.4, 2019, https://doi.org/10.12989/acc.2020.9.4.397
  2. Finite element based post-buckling analysis of refined graphene oxide reinforced concrete beams with geometrical imperfection vol.25, pp.4, 2020, https://doi.org/10.12989/cac.2020.25.4.283
  3. Multiphysical theoretical prediction and experimental verification of vibroacoustic responses of fruit fiber‐reinforced polymeric composite vol.41, pp.11, 2020, https://doi.org/10.1002/pc.25724
  4. Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method vol.76, pp.3, 2019, https://doi.org/10.12989/sem.2020.76.3.413
  5. A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications vol.11, pp.6, 2019, https://doi.org/10.12989/mwt.2020.11.6.399
  6. Stressing State Analysis of Reinforcement Concrete Beams Strengthened with Carbon Fiber Reinforced Plastic vol.14, pp.1, 2019, https://doi.org/10.1186/s40069-020-00417-w
  7. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2019, https://doi.org/10.12989/amr.2020.9.4.265
  8. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  9. Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers vol.37, pp.6, 2019, https://doi.org/10.12989/scs.2020.37.6.711
  10. Experimental and analytical study on continuous GFRP-concrete decks with steel bars vol.76, pp.6, 2019, https://doi.org/10.12989/sem.2020.76.6.737
  11. Effect of boundary conditions on thermal buckling of laminated composite shallow shell vol.42, pp.p5, 2021, https://doi.org/10.1016/j.matpr.2020.12.501
  12. Geometrical Influences on the Vibration of Layered Plates vol.2021, 2019, https://doi.org/10.1155/2021/8843358
  13. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2019, https://doi.org/10.12989/sem.2021.77.1.057
  14. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2019, https://doi.org/10.12989/sem.2021.77.2.217
  15. Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell vol.10, pp.2, 2019, https://doi.org/10.12989/anr.2021.10.2.175
  16. Dynamic damage analysis of a ten-layer circular composite plate subjected to low-velocity impact vol.21, pp.3, 2019, https://doi.org/10.1007/s43452-021-00238-y
  17. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2019, https://doi.org/10.12989/scs.2021.40.3.355
  18. Surface wave scattering analysis in an initially stressed stratified media vol.38, pp.8, 2019, https://doi.org/10.1108/ec-03-2020-0133
  19. Bending analysis of the multi-phase nanocomposite reinforced circular plate via 3D-elasticity theory vol.40, pp.4, 2021, https://doi.org/10.12989/scs.2021.40.4.601