Skip to main content
SpringerLink
Log in

Free vibration and transient analysis of advanced composite plates using a new higher-order shear and normal deformation theory

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

This article has been updated

Abstract

This study makes an attempt at analyzing free vibration and transient behavior of advanced composites such as FGM plates by isogeometric approach. A new hybrid-type HSDT capable of taking into account through-thickness expansion for the dynamic analysis is developed and coupled with the NURBS-based IGA method. The quasi-3D theory in which the transverse displacement is divided into the bending and shear terms employs the independent shear and normal shape functions. The Hamilton’s principle is used to derive the governing equilibrium equations for the dynamic problem. Some numerical examples available in the relevant literature are first simulated to verify the proposed quasi-3D analysis method, and their results are matched with the reference values. The accuracy and effectiveness of the present higher-order shear and normal deformation theory combined with the IGA method in obtaining solution for the free vibration and transient response are evidenced. Illustrative parametric studies are also performed to further investigate the effects of the plate geometric parameter, ingredient fraction, boundary condition and FGM constituents, all of which have significant influences on the dynamic and transient behavior.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Change history

  • 13 January 2021

    Journal abbreviated title on top of the page has been corrected to “Arch Appl Mech”

References

  1. Malekzadeh, P., Shahpari, S.A., Ziaee, H.R.: Three-dimensional free vibration of thick functionally graded annular plates in thermal environment. J. Sound Vib. 329, 425–442 (2010)

    Google Scholar 

  2. Rezaei Mojdehi, A., Darvizeh, A., Basti, A., Rajabi, H.: Three dimensional static and dynamic analysis of thick functionally graded plates by the meshless local Petrov-Galerkin (MLPG) method. Eng. Anal. Bound. Elem. 35, 1168–1180 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Su, Z., Jin, G., Ye, T.: Three-dimensional vibration analysis of thick functionallygraded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints. Compos. Struct. 118, 432–447 (2014)

    Google Scholar 

  4. Nguyen, K.D., Nguyen-Xuan, H.: An isogeometric finite element approach for three-dimensional static and dynamic analysis of functionally graded material plate structures. Compos. Struct. 132, 423–439 (2015)

    Google Scholar 

  5. Woo, J., Meguid, S.A., Ong, L.S.: Nonlinear free vibration behavior of functionally graded plates. J. Sound Vib. 289, 595–611 (2006)

    Google Scholar 

  6. Arefi, M.: The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers. Smart Struct. Syst. 15, 1345–1362 (2015)

    Google Scholar 

  7. Darilmaz, K.: Vibration analysis of functionally graded material (FGM) grid systems. Steel Compos. Struct. 18, 395–408 (2015)

    Google Scholar 

  8. Pradhan, K.K., Chakraverty, S.: Free vibration of functionally graded thin elliptic plates with various edge supports. Struct. Eng. Mech. 53, 337–354 (2015)

    Google Scholar 

  9. Ferreira, A.J.M., Castro, L.M., Bertoluzza, S.: A high order collocation method for the static and vibration analysis of composite plates using a first-order theory. Compos. Struct. 89, 424–432 (2009)

    Google Scholar 

  10. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H., Omidi, M.: Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl. Math. Model. 34, 1276–1291 (2010)

    MathSciNet  MATH  Google Scholar 

  11. Yin, S., Hale, J.S., Yu, T., Bui, T.Q., Bordas, S.P.A.: Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos. Struct. 118, 121–138 (2014)

    Google Scholar 

  12. Panda, S.K., Katariya, P.V.: Stability and free vibration behaviour of laminated composite panels under thermo-mechanical loading. Int. J. Appl. Comput. Math. 1, 475–490 (2015)

    MathSciNet  MATH  Google Scholar 

  13. Mantari, J.L., Granados, E.V.: Dynamic analysis of functionally graded plates using a novel FSDT. Compos. Part B Eng. 75, 148–155 (2015)

    Google Scholar 

  14. Mantari, J.L., Ore, M.: Free vibration of single and sandwich laminated composite plates by using a simplified FSDT. Compos. Struct. 132, 952–959 (2015)

    Google Scholar 

  15. Yu, T., Yin, S., Bui, T.Q., Xia, S., Tanaka, S., Hirose, S.: 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 Walled Struct. 101, 141–156 (2016)

    Google Scholar 

  16. Kiani, Y.: Free vibration of FG-CNT reinforced composite skew plates. Aerosp. Sci. Technol. 58, 178–188 (2016)

    Google Scholar 

  17. Singh, B.N., Yadav, D., Iyengar, N.G.R.: Natural frequencies of composite plates with random material properties using higher-order shear deformation theory. Int. J. Mech. Sci. 43, 2193–2214 (2001)

    MATH  Google Scholar 

  18. Zenkour, A.M.: A comprehensive analysis of functionally graded sandwich plates: part 2-Buckling and free vibration. Int. J. Solids Struct. 42, 5243–5258 (2005)

    MATH  Google Scholar 

  19. Aagaah, M.R., Mahinfalah, M., Jazar, G.N.: Natural frequencies of laminated composite plates using third order shear deformation theory. Compos. Struct. 72, 273–279 (2006)

    Google Scholar 

  20. Swaminathan, K., Patil, S.: Analytical solutions using a higher order refined computational model with 12 degrees of freedom for the free vibration analysis of antisymmetric angle-ply plates. Compos. Struct. 82, 209–216 (2008)

    Google Scholar 

  21. Xiang, S., Jin, Y., Bi, Z., Jiang, S., Yang, M.: A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates. Compos. Struct. 93, 2826–2832 (2011)

    Google Scholar 

  22. Mahi, A., Bedia, E.A.A., Tounsi, A.: 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 (2015)

    MathSciNet  MATH  Google Scholar 

  23. Gupta, A., Talha, M., Singh, B.N.: Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory. Compos. Part B Eng. 94, 64–74 (2016)

    Google Scholar 

  24. Karamanlı, A.: Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Compos. Struct. 189, 127–136 (2018)

    Google Scholar 

  25. Shi, P., Dong, C., Sun, F., Liu, W., Hu, Q.: A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis. Compos. Struct. 204, 342–358 (2018)

    Google Scholar 

  26. Taleb, O., Houari, M.S.A., Bessaim, A., Tounsi, A., Mahmoud, S.R.: A new plate model for vibration response of advanced composite plates in thermal environment. Struct. Eng. Mech. 67, 369–383 (2018)

    Google Scholar 

  27. Ansari, R., Torabi, J., Hassani, R.: A comprehensive study on the free vibration of arbitrary shaped thick functionally graded CNT-reinforced composite plates. Eng. Struct. 181, 653–669 (2019)

    Google Scholar 

  28. Bennai, R., Fourn, H., Atmane, H.A., Tounsi, A., Bessaim, A.: Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory. Wind Struct. Int. J. 28, 49–62 (2019)

    Google Scholar 

  29. Karami, B., Janghorban, M., Tounsi, A.: Galerkin’s approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Eng. Comput. 35, 1297–1316 (2019)

    Google Scholar 

  30. Soltani, K., Bessaim, A., Houari, M.S.A., Kaci, A., Benguediab, M., Tounsi, A., Alhodaly, M.S.: A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations. Steel Compos. Struct. 30, 13–29 (2019)

    Google Scholar 

  31. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, K.H., Tounsi, A.: Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory. Comput. Concr. 25, 225–244 (2020)

    Google Scholar 

  32. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, Tounsi, A.: Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundation. Comput. Concr. 25, 311–325 (2020)

    Google Scholar 

  33. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Tounsi, A.: Bending analysis of functionally graded porous plates via a refined shear deformation theory. Comput. Concr. 26, 63–74 (2020)

    Google Scholar 

  34. Daikh, A.A., Bensaid, I., Bachiri, A., Houari, M.S.A., Tounsi, A., Merzouki, T.: On static bending of multilayered carbon nanotube-reinforced composite plates. Comput. Concr. 26, 137–150 (2020)

    Google Scholar 

  35. Rabhi, M., Benrahou, K.H., Kaci, A., Houari, M.S.A., Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Tounsi, A.: A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary condition. Geomech. Eng. 22, 119–132 (2020)

    Google Scholar 

  36. Chikr, S.C., Kach, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, K.H., Tounsi, A.: A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin’s approach. Geomech. Eng. 21, 471–487 (2020)

    Google Scholar 

  37. Tounsi, A., Al-Dulaijan, S.U., Mohammed, A., Al-Osta, Chikh, A., Al-Zahrani, M.M., Sharif, A., Tounsi, A.: A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation. Steel Compos. Struct. 34, 511–524 (2020)

    Google Scholar 

  38. Menasria, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R.: A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions. Steel Compos. Struct. 36, 355–367 (2020)

    Google Scholar 

  39. Daikh, A.A., Bessaim, A., Houari, M.S.A., Tounsi, A.: Size dependent free vibration and buckling of multilayered carbon nanotubes reinforced composite nanoplates in thermal environment. Mech. Base Des. Struct. Mach. (2020). https://doi.org/10.1080/15397734.2020.1752232

    Article  Google Scholar 

  40. Daikh, A.A., Drai, A., Houari, M.S.A., Tounsi, A.: On vibration of functionally graded sandwich nanoplates in the thermal environment. J. Sandw. Struct. Mater. (2020). https://doi.org/10.1177/1099636220909790

    Article  Google Scholar 

  41. Carrera, E.: A study of transverse normal stress effect on vibration of multilayered plates and shells. J. Sound Vib. 225, 803–829 (1999)

    Google Scholar 

  42. Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. Part B Eng. 42, 123–133 (2011)

    Google Scholar 

  43. Zenkour, A.M.: Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Arch. Appl. Mech. 77, 197–214 (2007)

    MATH  Google Scholar 

  44. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N., Soares, C.M.N.: A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos. Part B Eng. 43, 711–725 (2012)

    Google Scholar 

  45. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., Soares, C.M.N.: A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Compos. Struct. 94, 1814–1825 (2012)

    Google Scholar 

  46. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., Soares, C.M.N.: Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. Part B Eng. 44, 657–674 (2013)

    Google Scholar 

  47. Houari, T., Bessaim, A., Houari, M.S.A., Benguediab, M., Tounsi, A.: Bending analysis of advanced composite plates using a new quasi 3D plate theory. Steel Compos. Struct. 26, 557–572 (2018)

    Google Scholar 

  48. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A., Mahmoud, S.R.: Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT. Adv. Nano Res. 7, 191–208 (2019)

    Google Scholar 

  49. Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A., Mahmoud, S.R.: Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter. Steel Compos. Struct. 28, 13–24 (2018)

    Google Scholar 

  50. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A., Mahmoud, S.R.: Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT. Comput. Concr. 24, 347–367 (2019)

    Google Scholar 

  51. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A., Al-Osta, M.A.: A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and Free vibration analysis. Comput. Concr. 25, 37–57 (2020)

    Google Scholar 

  52. Mantari, J.L., Guedes, Soares C.: Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates. Compos. Struct. 94, 2561–2575 (2012)

    Google Scholar 

  53. Mantari, J.L., Guedes, Soares C.: A novel higher-order shear deformation theory with stretching effect for functionally graded plates. Compos. Part B Eng. 45, 268–281 (2013)

    Google Scholar 

  54. Mantari, J.L., Guedes, Soares C.: A trigonometric plate theory with 5-unknowns and stretching effect for advanced composite plates. Compos. Struct. 107, 396–405 (2014)

    Google Scholar 

  55. Mantari, J.L., Granados, E.V.: Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns. Compos. Part B Eng. 69, 317–334 (2015)

    Google Scholar 

  56. Mantari, J.L., Granados, E.V.: Thermoelastic behavior of advanced composite sandwich plates by using a new 6 unknown quasi-3D hybrid type HSDT. Compos. Struct. 126, 132–144 (2015)

    Google Scholar 

  57. Thai, C.H., Zenkour, A., Wahab, M.A., Nguyen-Xuan, H.: A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis. Compos. Struct. 139, 77–95 (2016)

    Google Scholar 

  58. Senthilnathan, N.R., Lim, S.P., Lee, K.H., Chow, S.T.: Buckling of shear-deformable plates. AIAA J. 25, 1268–1271 (1987)

    Google Scholar 

  59. Kant, T., Swaminathan, K.: Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Compos. Struct. 53, 73–85 (2001)

    Google Scholar 

  60. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135–4195 (2005)

    MathSciNet  MATH  Google Scholar 

  61. Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Methods Eng. 47, 663–684 (2000)

    MATH  Google Scholar 

  62. Karama, M., Afaq, K.S., Mistou, S.: Mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity. Int. J. Solid Struct. 40, 1525–1546 (2003)

    MATH  Google Scholar 

  63. Fazzolari, F.A., Carrera, E.: Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions. J. Therm. Stress. 37, 1449–1481 (2014)

    Google Scholar 

  64. Auricchio, F., Beirao da Veiga, L., Buffa, A., Lovadina, C., Reali, A., Sangalli, G.: A fully locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation. Comput. Methods Appl. Mech. Eng. 197, 160–172 (2007)

    MathSciNet  MATH  Google Scholar 

  65. Li, Q., Iu, V.P., Kou, K.P.: Three-dimensional vibration analysis of functionally graded material sandwich plates. J. Sound Vib. 311, 498–515 (2008)

    Google Scholar 

  66. Malik, M., Bert, C.W.: Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method. Int. J. Solids Struct. 35, 299–318 (1998)

    MATH  Google Scholar 

  67. Zhu, P., Liew, K.M.: Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method. Compos. Struct. 93, 2925–2944 (2011)

    Google Scholar 

  68. Benachour, A., Tahara, H.D., Atmanea, H.A., Tounsia, A., Ahmed, M.S.: A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient. Compos. Part B Eng. 42(6), 1386–1394 (2011)

    Google Scholar 

  69. Sheikholeslami, S.A., Saidi, A.R.: Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory. Compos. Struct. 106, 350–361 (2013)

    Google Scholar 

  70. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Beg, O.A.: An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates. Compos. Part B Eng. 60, 274–283 (2014)

    Google Scholar 

  71. Akavci, S.S., Tanrikulu, A.H.: Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories. Compos. Part B Eng. 83, 203–215 (2015)

    Google Scholar 

  72. Tornabene, F.: Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Comput. Methods Appl. Mech. Eng. 198, 2911–2935 (2009)

    MATH  Google Scholar 

  73. Kiendl, J., Bazilevs, Y., Hsu, M.C., Wüchner, R., Bletzinger, K.U.: The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput. Methods Appl. Mech. Eng. 199, 2403–2416 (2010)

    MathSciNet  MATH  Google Scholar 

  74. Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35, 4457–4476 (1998)

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1075346).

Author information

Authors and Affiliations

  1. Applied Computational Civil and Structural Engineering Research Group, Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vuong Nguyen Van Do

  2. Department of Civil and Environmental Engineering, Daelim University College, 29, Imgok-ro, Dongan-ku, Anyang-si, Gyeonggi-do, 13916, Republic of Korea

    Chin-Hyung Lee

Authors
  1. Vuong Nguyen Van Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chin-Hyung Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chin-Hyung Lee.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Van Do, V.N., Lee, CH. Free vibration and transient analysis of advanced composite plates using a new higher-order shear and normal deformation theory. Arch Appl Mech 91, 1793–1818 (2021). https://doi.org/10.1007/s00419-020-01855-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01855-4

Keywords

Search

Navigation