Structural Engineering and Mechanics

  • 제49권5호
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  • Pages.537-554
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  • 2014
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Higher order free vibration of sandwich curved beams with a functionally graded core

  • Fard, K. Malekzadeh (Department of Structural Analysis and Simulation, Space Research Institute, Malek Ashtar University of Technology)
  • 투고 : 2013.07.25
  • 심사 : 2013.12.09
  • 발행 : 2014.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, free vibration of a sandwich curved beam with a functionally graded (FG) core was investigated. Closed-form formulations of two-dimensional (2D) refined higher order beam theory (RHOBT) without neglecting the amount of z/R was derived and used. The present RHOBT analysis incorporated a trapezoidal shape factor that arose due to the fact that stresses through the beam thickness were integrated over a curved surface. The solutions presented herein were compared with the available numerical and analytical solutions in the related literature and excellent agreement was obtained. Effects of some dimensionless parameters on the structural response were investigated to show their effects on fundamental natural frequency of the curved beam. In all the cases, variations of the material constant number were calculated and presented. Effect of changing ratio of core to beam thickness on the fundamental natural frequency depended on the amount of the material constant number.

키워드

참고문헌

  1. Ahmed, K.M. (1971), "Free vibration of curved sandwich beams by the method of finite elements", J. Sound. Vib., 18, 61-74. https://doi.org/10.1016/0022-460X(71)90631-6
  2. Apetre, N.A., Sankar, B.V. and Ambur, D.R. (2006), "Low-velocity impact of sandwich beams with functionally graded core", Int. J. Solid. Struct., 43(9), 2479-2496. https://doi.org/10.1016/j.ijsolstr.2005.06.003
  3. Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
  4. Auciello, N.M. and Rosa, M.A. (1994), "Free vibrations of circular arches: a review", J. Sound. Vib., 176, 433-458. https://doi.org/10.1006/jsvi.1994.1388
  5. Bao, G. and Wang, L. (1995), "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Solid. Struct., 32, 2853-2871. https://doi.org/10.1016/0020-7683(94)00267-Z
  6. Balasubramanian, T.S. and Prathap, G. (1989), "A field consistent higher-order curved beam element for static and dynamic analysis of stepped arches", J. Comput. Struct., 33, 281-288. https://doi.org/10.1016/0045-7949(89)90151-X
  7. Birman, V. (1995), "Stability of functionally graded hybrid composite plates", Compos. Eng., 5, 913-921. https://doi.org/10.1016/0961-9526(95)00036-M
  8. Chi, S.H. and Chung, Y.L. (2003), "Cracking in coating substrate composites of multi layered and sigmoid FGM coatings", Eng. Fract. Mech., 70, 1227-1243. https://doi.org/10.1016/S0013-7944(02)00114-5
  9. Eisenberger, M. and Efraim, E. (2001), "In-plane vibrations of shear deformable curved beams", Int. J. Numer. Meth. Eng., 52, 1221-1234. https://doi.org/10.1002/nme.246
  10. Garg, A.K., Khare, R.K. and Kant, T. (2006), "Higher-order closed-form solutions for free vibration of laminated composite and sandwich shells", J. Sandwich Struct. Mater., 8(3), 205-235. https://doi.org/10.1177/1099636206062569
  11. Golmakani, M.E. and Kadkhodayan, M.E. (2011), "Nonlinear bending analysis of annular FGM plates using higher-order shear deformation plate theories", Compos. Struct., 93, 973-982. https://doi.org/10.1016/j.compstruct.2010.06.024
  12. Kang, B., Riedel, C.H. and Tan, C.A. (2003), "Free vibration analysis of planar curved beams by wave propagation", J. Sound. Vib., 260, 19-44. https://doi.org/10.1016/S0022-460X(02)00898-2
  13. Henrych, J. (1981), The Dynamics of Arches, Elsevier Frames, New York.
  14. Khdeir, A.A. and Reddy, J.N. (1997), "Free and forced vibration of cross-ply laminated composite shallow arches", Int. J. Solid. Struct., 34, 1217-1234. https://doi.org/10.1016/S0020-7683(96)00095-9
  15. Kiani, Y., Akbarzadeh, A.H., Chen, Z.T. and Eslami, M.R. (2012), "Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak type elastic foundation", Compos. Struct., 94, 2474-2484. https://doi.org/10.1016/j.compstruct.2012.02.028
  16. Koizumi, M. (1993), "The concept of FGM ceramic transactions: functionally gradient materials", 34, 3-10.
  17. Khalili, S.M.R., Tafazoli, S. and Malekzadeh Fard, K. (2011), "Free vibrations of laminated composite shells with distributed uniformly attached mass using higher order shell theory including stiffness effect", J. Sound. Vib., 330(26), 6355-6371. https://doi.org/10.1016/j.jsv.2011.07.004
  18. Krishnan, A, Dharmaraj, S. and Suresh, Y.J. (1995), "Free vibration studies of arches", J. Sound. Vib., 186, 856-863. https://doi.org/10.1006/jsvi.1995.0493
  19. Krishnan, A. and Suresh, Y.J. (1998), "A simple cubic linear element for static and free vibration analyses of curved beams", J. Comput. Struct., 68, 473-489. https://doi.org/10.1016/S0045-7949(98)00091-1
  20. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams" , J. Sound. Vib., 318, 1210-29. https://doi.org/10.1016/j.jsv.2008.04.056
  21. Lu, Q. and Lu, C.F. (2008), "Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches", J. Sound. Vib., 318, 982-990. https://doi.org/10.1016/j.jsv.2008.05.011
  22. Malekzadeh, P. (2009), "Two-dimensional in-plane free vibrations of functionally graded circular arches with temperature-dependent properties", Compos. Struct., 91, 38-47. https://doi.org/10.1016/j.compstruct.2009.04.034
  23. Malekzadeh, P., Golbahar Haghighi, M.R. and Atashi, M.M. (2010), "Out of plane free vibration of functionally graded circular curved beam in thermal environment", Compos. Struct., 92, 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
  24. Marur, S.R. and Kant, T. (2008), "Free vibration of higher-order sandwich and composite arches, Part I: formulation" , J. Sound. Vib., 310(1-2), 91-109. https://doi.org/10.1016/j.jsv.2007.07.084
  25. Mori, T. and Tanaka, K. (1973), "Average stress in the matrix and average elastic energy of materials with misfitting inclusions", Acta Metall., 21, 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  26. Qatu, M.S. (1993), "Theories and analysis of thin and moderately thick laminated composite curved beams", Int. J. Solid. Struct., 30(3), 2743-2756. https://doi.org/10.1016/0020-7683(93)90152-W
  27. Sakiyama, T., Matsuda, H. and Morita, C. (1997), "Free vibration analysis of sandwich arches with elastic or visco elastic core and various kinds of axis shape and boundary conditions", J. Sound. Vib., 203, 505-522. https://doi.org/10.1006/jsvi.1996.0900
  28. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0
  29. Shen, H.S. (2009), Functionally Graded Materials-Nonlinear Analysis of Plates and Shells, CRC Press.
  30. Tseng, Y.P., Huang, C.S. and Kao, M.S. (2000), "In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis", J. Compos. Struct., 50, 103-114. https://doi.org/10.1016/S0263-8223(00)00003-9

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