Structural Engineering and Mechanics

  • 제45권4호
  • /
  • Pages.569-594
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  • 2013
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of tapered arches made of axially functionally graded materials

  • Rajasekaran, S. (Department of Civil Engineering, PSG College of Technology)
  • 투고 : 2011.08.06
  • 심사 : 2013.01.26
  • 발행 : 2013.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

The free vibration of axially functionally graded tapered arches including shear deformation and rotatory inertia are studied through solving the governing differential equation of motion. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal arches with hinged-hinged, hinged-clamped and clamped-clamped end restraints. In this study Differential Quadrature element of lowest order (DQEL) or Lagrangian Interpolation technique is applied to solve the problems. Three general taper types for rectangular section are considered. The lowest four natural frequencies are calculated and compared with the published results.

키워드

참고문헌

  1. Bellman, R. and Casti, J. (1971), "Differential quadrature and Long term Integration", J. Math. Anal. Appl., 34, 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
  2. Bert, C.W., Wang, X. and Striz, A.G. (1993), "Differential quadrature for static and free vibration analysis of anisotropic plates", Int. J. Solids. Struct., 30(13), 1737-1744. https://doi.org/10.1016/0020-7683(93)90230-5
  3. Bert, C.W., Wang, X. and Striz, A.G. (1994), "Static and free vibration analysis of beams and plates by differential quadrature method", Acta. Mech., 102, 11-24. https://doi.org/10.1007/BF01178514
  4. Borg, S.F. and Gennaro, J.J. (1959), Advanced Structural Analysis, Van Nostrand, Princeton, NJ.
  5. Boresi, A.P., Sidebottom, O.M., Seely, F.B. and Smith, J.O, (1978), Advanced Mechanics of Materials, John Wiley and sons, New York.
  6. Chidamparam, P. and Leissa, A.W. (1993), "Vibration of planar curved beams, rings and arches", Appl. Mech. Rev., 46 (9), 467-483. https://doi.org/10.1115/1.3120374
  7. Den Hartog, J.P. (1928), "The lowest natural frequencies of circular arcs", Philos. Mag., 75, 400-408.
  8. Friedman, Z. and Kosmatka, J.B, (1998), "An accurate two-node Finite Element for shear deformable curved beams", Int. J. Numer. Methods Eng, 41,473-498. https://doi.org/10.1002/(SICI)1097-0207(19980215)41:3<473::AID-NME294>3.0.CO;2-Q
  9. Gupta, A.K. (1985), "Vibration of tapered beams", J. Struct. Eng., ASCE, 111,19-36. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:1(19)
  10. Gutierrez, R.H., Laura, P.A.A., Rossi, R.E., Bertero, R. and Villaggi, A. (1989), "In-plane vibrations of noncircular arcs of non-uniform cross-section", J. Sound. Vib, 129, 181-200. https://doi.org/10.1016/0022-460X(89)90577-4
  11. Henrych, J. (1989), The dynamics of arches and frames, Elsevier, New York.
  12. Huang, C.S., Tseng, Y.P., Leissa, A.W. and Nieh, A.Y. (1998), "An exact solution for in plane vibrations of an arch having variable curvature and cross section", Int. J. Mech. Sci., 40(11), 1159-1173. https://doi.org/10.1016/S0020-7403(98)00020-4
  13. Irie, T., Yamada, G. and Tanaka, K. (1983), "Natural frequencies of in-plane vibration of arcs", J. Appl. Mech., 50(2), 449-452. https://doi.org/10.1115/1.3167058
  14. Kang, K., Bert, C.W. and Striz, A.G. (1995), "Vibration analysis of shear deformable circular arches by differential quadrature method", J. Sound. Vib., 183, 353-360. https://doi.org/10.1006/jsvi.1995.0258
  15. Kawakami, M., Sakiyama, T., Matsuda, H. and Morita, C. (1995), "In-plane and out-of-plane free vibrations of curved beams with variable sections", J. Sound Vib., 187, 381-401. https://doi.org/10.1006/jsvi.1995.0531
  16. Kim, J.G. and Lee, J.K. (2008), "Free vibration Analysis of arches based on the hybrid mixed formulation with consistent quadratic stress functions", Comput. Struct., 86(15-16), 1672-1681. https://doi.org/10.1016/j.compstruc.2007.07.002
  17. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans, Functionally Graded Materials, 34, 3-10.
  18. Koizumi, M. (1997), "FGM activities in Japan", Composites: part B, 28,1-4.
  19. Laura, P.A.A., Verniere De Irassar, P.L., Carnicer, R. and Bertero, R. (1988), "A Note on vibrations of a circumferential arch with thickness varying in a discontinuous fashion", J. Sound. Vib., 120, 95-105 https://doi.org/10.1016/0022-460X(88)90336-7
  20. Lawrence, J.D. (1972), A Catalog of special plane curves, Dover publishers.
  21. Lee, B.K. and Wilson, J.F. (1989), "Free vibration of arches with variable curvature", J. Sound Vib., 136, 75-89.
  22. Leontovich, V. (1959), Frames and Arches, Mc-Graw-Hill.
  23. Lockwood, E.H. (1961), A book of curves, Cambridge University Press.
  24. Malekzadeh, P. (2009), "Two dimensional in-plane free vibration of functionally graded circular arches with temperature dependent properties", Compos. Struct., 91(1), 38-47. https://doi.org/10.1016/j.compstruct.2009.04.034
  25. Malekzadeh, P. and Setoodeh, A.R. (2009), "DQM in-plane free vibration of laminated moderately thick circular deep arches", Adv. Eng. Softw., 40(9), 798-803. https://doi.org/10.1016/j.advengsoft.2009.01.011
  26. Malekzadeh, P., Atashi, M.M. and Karami, G. (2009), "In-plane free vibration of functionally graded circular arches with temperature dependent properties under thermal environment", J. Sound.Vib., 326(3- 5), 837-851. https://doi.org/10.1016/j.jsv.2009.05.016
  27. Malekzadeh, P., Golbahar, M.R. and Atashi, M.M. (2010), "Out of plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92(2),541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
  28. Malekzadeh, P. (2010), "Out-of-plane Free vibration Analysis of Functionally graded Circular curved beams supported on elastic foundation", Int. J. App. Mech, 2(3), 635-657. https://doi.org/10.1142/S175882511000069X
  29. Maurizi, M.J., Rossi, R.E. and Belles, P.M. (1991), "Lowest natural frequency of clamped circular arcs of linearly tapered width", J. Sound. Vib,, 144,357-361. https://doi.org/10.1016/0022-460X(91)90755-9
  30. Maurizi, M.J., Belles, P.M., Rossi, R.E. and De Rosa, M.A. (1993), "Free vibration of a three-centred arc clamped at the ends", J. Sound. Vib., 161,187-189. https://doi.org/10.1016/0022-460X(93)90478-T
  31. Oh, S.J., Lee, B.K. and Lee, I.W. (1998a), "Free vibrations of circular arches with variable cross-section considering shear deformations and rotatory inertia", Fifth Pacific Structural Steel Conference, Seoul, Korea, October.
  32. Oh, S.J., Lee. B.K., Lee, I.W. and Park, M.H. (1998b), "Free vibrations of noncircular arches considering rotatory inertia and shear deformation", Comput. Mech., Barcelona, Spain.
  33. Oh, S.J., Lee, B.K. and Lee, I.W. (2000), "Free vibrations of non-circular arches with non-uniform crosssection", Int. J. Solids. Struct., 37(36) , 4871-4891. https://doi.org/10.1016/S0020-7683(99)00194-8
  34. Piovan, M.T., Domini, S. and Ramirez, J.M. (2012), "In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beam", Compos. Struct., 94, 3194-3206. https://doi.org/10.1016/j.compstruct.2012.04.032
  35. Rajasekaran, S. (2007), "Symbolic computation and differential quadrature method- A boon to engineering analysis", Struct. Eng. Mech., 27(6), 713-739. https://doi.org/10.12989/sem.2007.27.6.713
  36. Rajasekaran, S. (2008), "Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods", Struct. Eng. Mech., 28(2), 221-238. https://doi.org/10.12989/sem.2008.28.2.221
  37. Romanelli, E. and Laura, P.A. (1972), "Fundamental frequencies of non-circular, elastic, hinged arcs", J. Sound. Vib., 24, 17-22. https://doi.org/10.1016/0022-460X(72)90118-6
  38. Schilling, R.L. and Harris, S.L. (2000), Applied Numerical Methods for Engineers using Matlab and C, Brooks/Cole, Thomson Learning.
  39. Shafiee, H., Naei, M. and Eslami, M. (2006), "In-plane and out-of -plane buckling of arches made of functionally graded material", Int. J. Mech. Sci, 48, 907-915. https://doi.org/10.1016/j.ijmecsci.2006.01.001
  40. Shahba, A., Attarnejad, R., Tavanaie Marvi, M. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Composites-part-B-Eng., 42(4), 801-808..
  41. Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli Beam made of axially Functionally graded material", Appl. Math. Model., 36, 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073
  42. Shahba, A., Attarnejad, R., Jandaghi Semnani, S. and Honarvar Gheitanbaf, H. (2012), "New shape functions for non uniform curved Timoshenko beam with arbitrarily varying curvature using basic displacement functions", Meccanica, DOI, 10.1007/s 11012-012-9591-9.
  43. Shu, C. (2000), Differential Quadrature and its application in Engineering, Springer, Berlin.
  44. Tufekci, E. and Arpaci, A. (1998), "Exact Solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects", J. Sound. Vib., 209(5), 845-856. https://doi.org/10.1006/jsvi.1997.1290
  45. Tufekci, E. and Dogruer, O.Y. (2006), "Out-of-plane free vibration of a circular arch with uniform cross section: Exact solution", J. Sound. Vib., 291(3-5),525-538. https://doi.org/10.1016/j.jsv.2005.06.008
  46. Valetsos, A.S., Austin, W.J., Pereia, C.A.L. and Wung, S.J. (1972), "Free in-plane vibration of Circular Arches", J. Eng. Mech-ASCE., 98 (2), 311-329.
  47. Volterra, E. and Morell, J.D. (1960), "A Note on the lowest natural frequency of elastic arcs", J. Appl. Mech., 27, 744-746. https://doi.org/10.1115/1.3644096
  48. Wang, T.M. (1975), "Effect of variable curvature on fundamental frequency of clamped parabolic arcs", J. Sound. Vib., 41,247-251. https://doi.org/10.1016/S0022-460X(75)80100-3
  49. Wilson, E.L. (2002), Three Dimensional Static and Dynamic Analysis of Structures, Computers and Structures Inc., Berleley, California.
  50. Wilson, J.F., Lee, B.K. and Oh, S.J. (1994), "Free vibrations of circular arches with variable cross-section", Struct. Eng. Mech, 2(4), 345-357. https://doi.org/10.12989/sem.1994.2.4.345
  51. Wolf. Jr., J.A. (1971), "Natural Frequencies of Circular Arches", J. Struct. Eng-ASCE., 97(9), 2337-2350.
  52. Yousefi, A. and Rastgoo, A. (2011), "Free vibration of functionally graded spatial curved beams", Compos. Struct., 93(11), 3048-3056. https://doi.org/10.1016/j.compstruct.2011.04.024
  53. Zhao, Y. and Kang, H. (2008), "In-plane free vibration analysis of cable-arch structure", J. Sound. Vib., 312(3), 363-379. https://doi.org/10.1016/j.jsv.2007.04.038

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