DOI QR코드

DOI QR Code

A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass

  • Draiche, Kada (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) ;
  • Khalfi, Y. (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • 투고 : 2013.07.15
  • 심사 : 2014.02.16
  • 발행 : 2014.07.25

초록

The novelty of this paper is the use of trigonometric four variable plate theory for free vibration analysis of laminated rectangular plate supporting a localized patch mass. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The Hamilton's Principle, using trigonometric shear deformation theory, is applied to simply support rectangular plates. Numerical examples are presented to show the effects of geometrical parameters such as aspect ratio of the plate, size and location of the patch mass on natural frequencies of laminated composite plates. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of laminated rectangular plate supporting a localized patch mass.

키워드

참고문헌

  1. Alibakhshi, R. (2012), "The effect of anisotropy on free vibration of rectangular composite plates with patch mass", Int. J. Eng. Transactions B: Applications, 25(3), 223-232.
  2. Alibeigloo, A. and Kari, M.R. (2009), "Forced vibration analysis of anti-symmetric laminated rectangular plates with distributed patch mass using third order shear deformation theory", Thin-Wall. Struct., 47(6-7), 653-660. https://doi.org/10.1016/j.tws.2008.11.006
  3. Alibeigloo, A., Shakeri, M. and Kari, M.R. (2008), "Free vibration analysis of antisymmetric laminated rectangular plates with distributed patch mass using third-order shear deformation theory", J. Ocean Eng., 35(2), 183-190. https://doi.org/10.1016/j.oceaneng.2007.09.002
  4. Ambartsumian, S.A. (1958), "On the theory of bending plates", Izv Otd Tech Nauk AN SSSR, 5, 69-77.
  5. Bert, C.W. and Chen, T.L.C. (1978), "Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates", Int. J. Solid. Struct., 14(6), 465-473. https://doi.org/10.1016/0020-7683(78)90011-2
  6. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  7. Kant, T. and Swaminathan, K. (2001), "Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory", Compos. Struct., 53(1), 73-85. https://doi.org/10.1016/S0263-8223(00)00180-X
  8. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  9. Kim, S.E., Thai, H.T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89(2), 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017
  10. Leissa, A.W. (1969), "Vibration of plates. NASA, SP-160, O/ce of Technology Utilization", NASA, Washington, D.C., USA.
  11. Meirovitch, L. (2001), Fundamentals of Vibrations, McGraw Hill International Edition, Singapore.
  12. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38.
  13. Moradi, S. and Mansouri, M.H. (2012), "Thermal buckling analysis of shear deformable laminated orthotropic plates by differential quadrature", Steel Compos. Struct., Int. J., 12(2), 129-147. https://doi.org/10.12989/scs.2012.12.2.129
  14. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6
  15. Noor, A.K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868
  16. Rashidi, M.M., Shooshtari, A. and Anwar Beg, O. (2012) "Homotopy perturbation study of nonlinear vibration of Von Karman rectangular plates", Comput. Struct., 106-107, 46-55. https://doi.org/10.1016/j.compstruc.2012.04.004
  17. Reddy, J.N. (1979), "Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation by the finite element method", J. Sound Vib., 66(4), 565-576. https://doi.org/10.1016/0022-460X(79)90700-4
  18. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  19. Reddy, J.N. (1999), Theory and Analysis of Elastic Plates, Taylor & Francis, Philadelphia, PA, USA.
  20. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-77.
  21. Shankara, C.A. and Iyengar, N.G. (1996), "A $C^{\circ}$ element for the free vibration analysis of laminated composite plates", J. Sound Vib., 191(5), 721-738. https://doi.org/10.1006/jsvi.1996.0152
  22. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622
  23. Shimpi, R.P. and Patel, H.G. (2006a), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct., 43(22), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  24. Shimpi, R.P. and Patel, H.G. (2006b), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030
  25. Singh, B.N., Yadav, D. and Iyengar, N.G.R. (2001), "Natural frequencies of composite plates with random material properties using higher-order shear deformation theory", Int. J. Mech. Sci., 43(10), 2193-2214. https://doi.org/10.1016/S0020-7403(01)00046-7
  26. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3-4), 195-200. https://doi.org/10.1007/BF01176650
  27. Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 25(1-4), 165-171. https://doi.org/10.1016/0263-8223(93)90162-J
  28. Szilard, R. (1974), Theory and Analysis of Plates, Classical and Numerical Method, Prentice-Hall, Englewood Clils, NJ, USA.
  29. Timoshenko, S.P. (1955), Vibration Problems in Engineering, Van Nostrand, Princeton, NJ, USA.
  30. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  31. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  32. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0

피인용 문헌

  1. Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory vol.19, pp.1, 2015, https://doi.org/10.12989/scs.2015.19.1.093
  2. A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations vol.53, pp.6, 2015, https://doi.org/10.12989/sem.2015.53.6.1215
  3. A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation vol.20, pp.2, 2016, https://doi.org/10.12989/scs.2016.20.2.227
  4. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory vol.18, pp.4, 2016, https://doi.org/10.12989/sss.2016.18.4.755
  5. Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.245
  6. Experimental observation and energy based analytical investigation of matrix cracking distribution pattern in angle-ply laminates vol.92, 2017, https://doi.org/10.1016/j.tafmec.2017.06.007
  7. Static and dynamic behavior of FGM plate using a new first shear deformation plate theory vol.57, pp.1, 2016, https://doi.org/10.12989/sem.2016.57.1.127
  8. Effect of shear deformation on adhesive stresses in plated concrete beams: Analytical solutions vol.15, pp.3, 2015, https://doi.org/10.12989/cac.2015.15.3.337
  9. On the bending and stability of nanowire using various HSDTs vol.3, pp.4, 2015, https://doi.org/10.12989/anr.2015.3.4.177
  10. Dynamic behavior of FGM beam using a new first shear deformation theory vol.10, pp.2, 2016, https://doi.org/10.12989/eas.2016.10.2.451
  11. Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory vol.22, pp.4, 2016, https://doi.org/10.12989/was.2016.22.4.429
  12. Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations vol.40, 2015, https://doi.org/10.1016/j.ast.2014.11.005
  13. On vibration behavior of rotating functionally graded double-tapered beam with the effect of porosities vol.230, pp.10, 2016, https://doi.org/10.1177/0954410015619647
  14. Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.963
  15. A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.743
  16. Free vibration analysis of a rotating non-uniform functionally graded beam vol.19, pp.5, 2015, https://doi.org/10.12989/scs.2015.19.5.1279
  17. Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method vol.30, pp.6, 2016, https://doi.org/10.1007/s12206-016-0506-x
  18. An efficient shear deformation theory for wave propagation of functionally graded material plates vol.57, pp.5, 2016, https://doi.org/10.12989/sem.2016.57.5.837
  19. Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories vol.53, pp.6, 2015, https://doi.org/10.12989/sem.2015.53.6.1143
  20. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  21. A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates vol.56, pp.2, 2015, https://doi.org/10.12989/sem.2015.56.2.223
  22. Influence of the porosities on the free vibration of FGM beams vol.21, pp.3, 2015, https://doi.org/10.12989/was.2015.21.3.273
  23. A new higher order shear and normal deformation theory for functionally graded beams vol.18, pp.3, 2015, https://doi.org/10.12989/scs.2015.18.3.793
  24. A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates vol.22, pp.2, 2016, https://doi.org/10.12989/scs.2016.22.2.257
  25. An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations vol.22, pp.3, 2016, https://doi.org/10.12989/was.2016.22.3.329
  26. Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory vol.18, pp.2, 2015, https://doi.org/10.12989/scs.2015.18.2.443
  27. A new higher order shear deformation model for functionally graded beams vol.20, pp.5, 2016, https://doi.org/10.1007/s12205-015-0252-0
  28. Nonlinear Flexural Analysis of Laminated Composite Panel Under Hygro-Thermo-Mechanical Loading — A Micromechanical Approach vol.13, pp.03, 2016, https://doi.org/10.1142/S0219876216500158
  29. Analytical solution for bending analysis of functionally graded beam vol.19, pp.4, 2015, https://doi.org/10.12989/scs.2015.19.4.829
  30. Thermal Buckling Response of Functionally Graded Plates with Clamped Boundary Conditions vol.38, pp.6, 2015, https://doi.org/10.1080/01495739.2015.1015900
  31. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  32. A refined theory with stretching effect for the flexure analysis of laminated composite plates vol.11, pp.5, 2016, https://doi.org/10.12989/gae.2016.11.5.671
  33. Thermal stability of functionally graded sandwich plates using a simple shear deformation theory vol.58, pp.3, 2016, https://doi.org/10.12989/sem.2016.58.3.397
  34. Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel vol.29, pp.1, 2016, https://doi.org/10.1016/j.cja.2015.12.007
  35. An analytical method for free vibration analysis of functionally graded sandwich beams vol.23, pp.1, 2016, https://doi.org/10.12989/was.2016.23.1.059
  36. Dynamic behavior of piezoelectric composite beams under moving loads vol.50, pp.7, 2016, https://doi.org/10.1177/0021998315583319
  37. Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.357
  38. Postbuckling analysis of laminated composite shells under shear loads vol.21, pp.2, 2016, https://doi.org/10.12989/scs.2016.21.2.373
  39. Hybrid analysis and optimization of hierarchical stiffened plates based on asymptotic homogenization method vol.132, 2015, https://doi.org/10.1016/j.compstruct.2015.05.012
  40. Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1287
  41. Flexure of power law governed functionally graded plates using ABAQUS UMAT vol.46, 2015, https://doi.org/10.1016/j.ast.2015.06.021
  42. Research on mechanical properties of a polymer membrane with a void based on the finite deformation theory vol.15, pp.5, 2015, https://doi.org/10.1515/epoly-2015-0086
  43. A new simple shear and normal deformations theory for functionally graded beams vol.18, pp.2, 2015, https://doi.org/10.12989/scs.2015.18.2.409
  44. A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position vol.8, pp.3, 2015, https://doi.org/10.12989/gae.2015.8.3.305
  45. A computational shear displacement model for vibrational analysis of functionally graded beams with porosities vol.19, pp.2, 2015, https://doi.org/10.12989/scs.2015.19.2.369
  46. Interfacial stress analysis of functionally graded beams strengthened with a bonded hygrothermal aged composite plate vol.24, pp.2, 2017, https://doi.org/10.1080/09276440.2016.1196333
  47. On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model vol.18, pp.4, 2015, https://doi.org/10.12989/scs.2015.18.4.1063
  48. A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.547
  49. On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams vol.19, pp.5, 2015, https://doi.org/10.12989/scs.2015.19.5.1259
  50. A new higher-order shear and normal deformation theory for functionally graded sandwich beams vol.19, pp.3, 2015, https://doi.org/10.12989/scs.2015.19.3.521
  51. Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1347
  52. Realization of MOEMS pressure sensor using mach zehnder interferometer vol.29, pp.9, 2015, https://doi.org/10.1007/s12206-015-0829-z
  53. Investigation of the effects of viscous damping mechanisms on structural characteristics in coupled shear walls vol.116, 2016, https://doi.org/10.1016/j.engstruct.2016.02.031
  54. Electro-Magneto-Elastic Response of Laminated Composite Plate: A Finite Element Approach vol.3, pp.3, 2017, https://doi.org/10.1007/s40819-016-0256-6
  55. Static bending and free vibration of FGM beam using an exponential shear deformation theory vol.4, pp.1, 2015, https://doi.org/10.12989/csm.2015.4.1.099
  56. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.617
  57. Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position vol.38, pp.1, 2016, https://doi.org/10.1007/s40430-015-0354-0
  58. Effect of fiber tension on the deformation of a carbon composite plate for space radio telescopes vol.45, 2015, https://doi.org/10.1016/j.ast.2015.04.019
  59. Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory vol.18, pp.6, 2015, https://doi.org/10.12989/scs.2015.18.6.1493
  60. Determination of Optimum Process Parameters for Cutting Hole in a Randomly-oriented Glass Fiber Reinforced Epoxy Composite by Milling Process: Maximization of Surface Quality and Cut-hole Strength vol.24, pp.2, 2016, https://doi.org/10.1177/096739111602400201
  61. Determination of Optimum Process Parameters for Cutting Hole in a Randomly-oriented Glass Fiber Reinforced Epoxy Composite by Milling Process: Maximization of Surface Quality and Cut-hole Strength vol.24, pp.2, 2016, https://doi.org/10.1177/096739111602400201
  62. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2014, https://doi.org/10.12989/gae.2017.12.1.009
  63. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams vol.19, pp.2, 2017, https://doi.org/10.12989/sss.2017.19.2.115
  64. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2014, https://doi.org/10.12989/sss.2017.19.3.289
  65. Displacement Analytical Solution of a Circular Hole in Layered Composite Materials considering Shear Stress Effect vol.26, pp.3, 2014, https://doi.org/10.1177/096369351702600303
  66. Free vibrations of laminated composite plates using a novel four variable refined plate theory vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.603
  67. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  68. Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure vol.7, pp.3, 2019, https://doi.org/10.12989/anr.2019.7.3.181
  69. Dynamic symmetrical mode III interface crack issues between unalike materials vol.8, pp.3, 2019, https://doi.org/10.1680/jemmr.16.00064
  70. Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory vol.24, pp.6, 2019, https://doi.org/10.12989/cac.2019.24.6.489
  71. A Novel Refined Shear Deformation Theory for the Buckling Analysis of Thick Isotropic and Orthotropic Plates on Two-Parameter Pasternak’s Foundations vol.20, pp.1, 2014, https://doi.org/10.1007/s11668-019-00713-y
  72. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2014, https://doi.org/10.12989/scs.2021.40.3.355