DOI QR코드

DOI QR Code

Vibration of angle-ply laminated composite circular and annular plates

  • Mercan, Kadir (kdeniz University, Engineering Faculty, Division of Mechanics) ;
  • Ebrahimi, Farzad (Imam Khomeini International University, Mechanical Engineering Dept.) ;
  • Civalek, Omer (China Medical University, Research Center for Interneural Computing)
  • Received : 2019.07.07
  • Accepted : 2019.11.16
  • Published : 2020.01.10

Abstract

In the present paper, free vibration analysis of angle-ply laminated composite annular and circular plates is performed by numerical methods. First-order shear deformation plate theory is used for kinematic relations. The related governing equations of motion are discretized via differential quadrature and discrete singular convolution methods. Frequency values are obtained for different lamina scheme, thickness-to-radius ratio, and mode numbers. The advantages and accuracy of these two methods are also tested in detail.

Keywords

Acknowledgement

Supported by : China Medical University of Taiwan

This work was partially supported by the Research Center for Interneural Computing of China Medical University of Taiwan. Ö mer Civalek would like to thank the committee member of Research Center for Interneural Computing of China Medical University of Taiwan for their help during solution of some mathematical equations.

References

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693
  2. Akgoz, B. and Civalek, O. (2012), "Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory", Arch. Appl. Mech. 82, 423-443. https://doi.org/10.1007/s00419-011-0565-5
  3. Akgoz, B. and Civalek, O. (2017), "Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams", Compos. Part B: Eng, 129, 77-87. https://doi.org/10.1016/j.compositesb.2017.07.024
  4. Aleksandrova, N.N. (2016), "Effect of thermal gradients on stress/strain distributions in a thin circular symmetric plate", Struct. Eng. Mech., 58(4), 627-639. https://doi.org/10.12989/sem.2016.58.4.627
  5. Arefi, M., Mohammadi, M., Tabatabaeian, A., Dimitri, R. and Tornabene, F. (2018), "Two-dimensional thermo-elastic analysis of FG-CNTRC cylindrical pressure vessels", Steel Compos. Struct., 27(4), 525-536. https://doi.org/10.12989/scs.2018.27.4.525
  6. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  7. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871
  8. Azimi, S. (1988), "Free vibration of circular plates with elastic edge supports using the receptance method", J. Sound Vib., 120 (1) 19-35. https://doi.org/10.1016/0022-460X(88)90332-X.
  9. Baltacioglu, A.K., Akgoz, B. and Civalek, O. (2010), "Nonlinear static response of laminated composite plates by discrete singular convolution method", Compos. Struct., 93, 153-161. https://doi.org/10.1016/j.compstruct.2010.06.005.
  10. Baltacioglu, A.K., Civalek, O., Akgoz, B. and Demir, F. (2011), "Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution", Int. J. Pres. Ves. Pip., 88, 290-300. https://doi.org/10.1016/j.ijpvp.2011.06.004.
  11. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019.
  12. Bisadi, H., Eshaghi, M., Rokni, H., et al. (2012), "Benchmark solution for transverse vibration of annular Reddy plates", Int. J. Mech. Sci., 56(1), 35-49. https://doi.org/10.1016/j.ijmecsci.2011.12.007.
  13. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493- 1515. https://doi.org/10.12989/scs.2015.18.6.1493.
  14. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397.
  15. Civalek, O. (2007), "Linear vibration analysis of isotropic conical shells by discrete singular convolution (DSC)", Struct Eng Mech., 25(1), 127-130. https://doi.org/10.12989/sem.2007.25.1.127.
  16. Civalek, O. (1998), "Finite Element analysis of plates and shells", MSc Dissertation, Firat University, Elazig. (in Turkish).
  17. Civalek, O. (2004), "Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)", Ph.D. Dissertation, Firat University, Elazig. (in Turkish).
  18. Civalek, O. (2006a), "Free vibration analysis of composite conical shells using the discrete singular convolution algorithm", Steel Compos. Struct., 6(4), 353-366. https://doi.org/10.12989/scs.2006.6.4.353.
  19. Civalek, O. (2006b), "The determination of frequencies of laminated conical shells via the discrete singular convolution method", J. Mech. Mater. Struct., 1(1), 163-182. http://dx.doi.org/10.2140/jomms.2006.1.163.
  20. Civalek, O. (2008a), "Vibration analysis of conical panels using the method of discrete singular convolution", Commun. Numer. Meth. Eng., 24, 169-181. https://doi.org/10.1002/cnm.961.
  21. Civalek, O. (2008b), "Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory", J. Compos. Mater., 42, 2853-2867. https://doi.org/10.1177%2F0021998308096952. https://doi.org/10.1177/0021998308096952
  22. Civalek, O. (2013a), "Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches", Compos. Part B: Eng., 50, 171-179. https://doi.org/10.1016/j.compositesb.2013.01.027.
  23. Civalek, O. (2013b), "Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory", Compos. Part B: Eng., 45(1), 1001-1009. https://doi.org/10.1016/j.compositesb.2012.05.018.
  24. Civalek, O. (2017), "Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method", Compos. Part B: Eng., 111, 45-59. https://doi.org/10.1016/j.compositesb.2016.11.030.
  25. Civalek, O. and Akgoz, B. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403.
  26. Civalek, O. and Acar, M.H. (2007), "Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations", Int. J. Pres. Ves. Pip., 84, 527-535. https://doi.org/10.1016/j.ijpvp.2007.07.001.
  27. Civalek, O. and Demir, C. (2011), "Bending analysis of microtubules using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 35, 2053-2067. https://doi.org/10.1016/j.apm.2010.11.004.
  28. Civalek, O. and Demir, C. (2016), "A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method", Appl. Math. Comput., 289,335-352. https://doi.org/10.1016/j.amc.2016.05.034.
  29. Civalek, O., Korkmaz, A. and Demir, C. (2010), "Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges", Adv. Eng. Softw., 41, 557-560. https://doi.org/10.1016/j.advengsoft.2009.11.002.
  30. Civalek, O., Mercan, K. and Demir, C. (2016), "Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique", Curved Layer. Struct., 3, 82-90. https://doi.org/10.1515/cls-2016-0007.
  31. Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016.
  32. Demir, C., Mercan, K. and Civalek, O. (2016), "Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel", Compos. Part B Eng., 94, 1-10. https://doi.org/10.1016/j.compositesb.2016.03.031.
  33. Duan, G., Wang, X. and Jin, C. (2014), "Free vibration analysis of circular thin plates with stepped thickness by the DSC element method", Thin Wall. Struct., 85, 25-33. https://doi.org/10.1016/j.tws.2014.07.010.
  34. Fantuzzi, N. and Tornabene, F. (2014), "Strong formulation finite element method for arbitrarily shaped laminated plates- Part I. Theoretical analysis", Adv. Aircr. Spacecr. Sci., 1(2), 125-143. http://dx.doi.org/10.12989/aas.2014.1.2.125.
  35. Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219, 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062.
  36. Gurses, M., Civalek, O., Korkmaz, A. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory", Int. J. Numer. Method. Eng., 79, 290-313. https://doi.org/10.1002/nme.2553.
  37. Hamzehkolaei, N.S., Malekzadeh, P. and Vaseghi, J. (2011), "Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM", Steel Compos. Struct., \11(4), 341-358. https://doi.org/10.12989/scs.2011.11.4.341.
  38. Hou, Y., Wei, G.W. and Xiang, Y. (2005), "DSC-Ritz method for the free vibration analysis of Mindlin plates", Int. J. Numer. Meth. Eng., 62, 262-288. https://doi.org/10.1002/nme.1186.
  39. Jhung, M.J., Choi, Y.H. and Kim, H.J. (2005), "Natural vibration characteristics of a clamped circular plate in contact with fluid", Struct. Eng. Mech., 21(2), 169-184. https://doi.org/10.12989/sem.2005.21.2.169.
  40. Khare, S. and Mittal, N.D. (2016), "Three-dimensional free vibration analysis of thick laminated circular plates", Int. J. Eng., Sci. Technol., 8(2), 11-29. http://dx.doi.org/10.4314/ijest.v8i2.2.
  41. Khare, S. and Mittal, N.D. (2018), "Free vibration of thick laminated circular and annular plates using three-dimensional finite element analysis", AEJ - Alexandria Eng. J., 57(3), 1217-1228. https://doi.org/10.1016/j.aej.2017.03.006.
  42. Leissa, A.W. (1993), Vibration of shells, Acoustical Society of America, Melville, NY, USA.
  43. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick laminated annular sector plates using a hybrid method", Compos. Struct., 90, 428-437. https://doi.org/10.1016/j.compstruct.2009.04.015.
  44. Mehditabar, A., Rahimi, G.H. and Fard, K.M. (2018), "Vibrational responses of antisymmetric angle-ply laminated conical shell by the methods of polynomial based differential quadrature and Fourier expansion based differential quadrature", Appl. Math. Comput., 320, 580-595. https://doi.org/10.1016/j.amc.2017.10.017.
  45. Mercan, K. and Civalek, O. (2016), "DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Compos. Struct., 143, 300-309. https://doi.org/10.1016/j.compstruct.2016.02.040.
  46. Mercan, K. and Civalek, O. (2017), "Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ", Compos. Part B: Eng., 114, 34-45. https://doi.org/10.1016/j.compositesb.2017.01.067.
  47. Pang, F., Li, H., Miao, X. and Wang, X. (2017), "A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports", Curved Layer. Struct., 4, 189-220. https://doi.org/10.1515/cls-2017-0014.
  48. Qatu, M. (2004), Vibration Of Laminated Shells And Plates, Academic Press, U.K.
  49. Reddy, J.N. (2003), Mechanics Of Laminated Composite Plates And Shells: Theory And Analysis, (2nd edition), CRC Press, New York, NY, USA.
  50. Saidi, A.R., Baferani, A.H. and Jomehzadeh, E. (2011), "Benchmark solution for free vibration of functionally graded moderately thick annular sector plates", Acta Mech., 219, 309-335. https://doi.org/10.1007/s00707-011-0459-1.
  51. Sharma, A., Sharda, H.B. and Nath, Y. (2005), "Stability and vibration of thick laminated composite sector plates", J. Sound Vib., 287, 1-23. https://doi.org/10.1016/j.jsv.2004.10.030.
  52. Shu, C. and Xue, H. (1997), "Explicit computations of weighting coefficients in the harmonic differential quadrature", J. Sound Vib., 204(3), 549-555. https://doi.org/10.1006/jsvi.1996.0894.
  53. Soedel, W. (2004), Vibrations of shells and plates, (3rd edition), CRC Press, New York, NY, USA.
  54. Striz, A.G., Wang, X. and Bert, C.W. (1995), "Harmonic differential quadrature method and applications to analysis of structural components", Acta Mech., 111, 85-94. https://doi.org/10.1007/BF01187729.
  55. Su, Z., Jin, G. and Wang X. (2015), "Free vibration analysis of laminated composite and functionally graded sector plates with general boundary conditions", Compos. Struct., 132, 720-736. https://doi.org/10.1016/j.compstruct.2015.06.008.
  56. Su, Z., Jin, G. and Ye, T. (2014), "Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints", Compos. Struct., 118, 432-447. https://doi.org/10.1016/j.compstruct.2014.07.049
  57. Tahouneh, V. (2014), "Free vibration analysis of bidirectional functionally graded annular plates resting on elastic foundations using differential quadrature method", Struct. Eng. Mech., 52(4), 663-686. https://doi.org/10.12989/sem.2014.52.4.663
  58. Tornabene, F. and Fantuzzi, N. (2014), Mechanics of laminated composite doubly-curved shell structures, the generalized differential quadrature method and the strong formulation finite element method. Societa Editrice Esculapio, Bologna, Italy.
  59. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: the free vibration analysis", Compos. Struct., 116, 637-660. https://doi.org/10.1016/j.compstruct.2014.05.008
  60. Tornabene, F., Fantuzzi, N., Bacciocchi, M. and Viola, E. (2016), "Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells", Compos. Part B: Eng., 89, 187-218. https://doi.org/10.1016/j.compositesb.2015.11.016.
  61. Tornabene, F., Fantuzzi, N., Viola, E. and Ferreira, A.J.M. (2013), "Radial basis function method applied to doubly-curved laminated composite shells and panels with a General Higherorder Equivalent Single Layer formulation", Compos. Part B: Eng., 55, 642-659. https://doi.org/10.1016/j.compositesb.2013.07.026.
  62. Viswanathan, K.K. and Sheen, D. (2009), "Free vibration of layered annular circular plate of variable thickness using spline function approximation", Indian J. Eng. Mater. Sci., 16, 433-448.
  63. Viswanathan, K.K., Javed, S., Prabakar, K., Aziz, Z.A. and Bakar, I.A. (2015), "Free vibration of anti-symmetric angle-ply laminated conical shells", Compos. Struct., 122, 488-495. https://doi.org/10.1016/j.compstruct.2014.11.075.
  64. Viswanathan, K.K., Javed, S. and Zainal A.A. (2013), "Free vibration of antisymmetric angle-ply laminated annular circular pplate", Proceedings of the World Congress on Engineering, Vol III, WCE 2013, July 3 - 5, London.
  65. Wang, Q., et al. (2016b), "A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions", Appl. Math. Model., 40(21), 9228-9253. https://doi.org/10.1016/j.apm.2016.06.005.
  66. Wang, Q., Shi, D., Liang, Q. and Ahad, F. (2016a), "An improved Fourier series solution for the dynamic analysis of laminated composite annular, circular, and sector plate with general boundary conditions", J. Comp. Mater., 50(30), 4199-4233. https://doi.org/10.1177%2F0021998316635240. https://doi.org/10.1177/0021998316635240
  67. Wang, X., Wang, Y. and Xu, S. (2012), "DSC analysis of a simply supported anisotropic rectangular plate", Compos. Struct., 94, 2576-2584. https://doi.org/10.1016/j.compstruct.2012.03.005.
  68. Wei, G.W. (2001a), "Vibration analysis by discrete singular convolution", J. Sound Vib., 244, 535-553. https://doi.org/10.1006/jsvi.2000.3507.
  69. Wei, G.W. (2001b), "Discrete singular convolution for beam analysis", Eng. Struct., 23, 1045-1053. https://doi.org/10.1016/S0141-0296(01)00016-5.
  70. Wei, G.W., Zhao, Y.B. and Xiang, Y. (2001), "The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution" Int. J. Mech. Sci., 43, 1731-1746. https://doi.org/10.1016/S0020-7403(01)00021-2.
  71. Wei, G.W., Zhao, Y.B. and Xiang, Y. (2002a), "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib., 257, 207-246. https://doi.org/10.1006/jsvi.2002.5055.
  72. Wei, G.W., Zhao, Y.B. and Xiang, Y. (2002b),"Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm", Int. J. Numer. Meth. Eng., 55, 913-946. https://doi.org/10.1002/nme.526.
  73. Wu, C.P. and Yu, L.T. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161
  74. Wu, C.P. and Yu, L.T., (2018), "Quasi-3D static analysis of twodirectional functionally graded circular plates", Steel Compos Struct., 27(6), 789-801. https://doi.org/10.12989/scs.2018.27.6.789
  75. Yousefzadeh, Sh., Jafari, A.A., Mohammadzadeh, A., et al. (2018), "Dynamic response of functionally graded annular/circular plate in contact with bounded fluid under harmonic load", Struct. Eng. Mech., 65(5), 523-533. https://doi.org/10.12989/sem.2018.65.5.523

Cited by

  1. On the free vibration response of laminated composite plates via FEM vol.39, pp.2, 2020, https://doi.org/10.12989/scs.2021.39.2.149
  2. 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
  3. A new model for adhesive shear stress in damaged RC cantilever beam strengthened by composite plate taking into account the effect of creep and shrinkage vol.79, pp.5, 2020, https://doi.org/10.12989/sem.2021.79.5.531