Structural Engineering and Mechanics

  • 제53권5호
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  • Pages.981-995
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  • 2015
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads

  • Gan, Buntara S. (Department of Architecture, College of Engineering, Nihon University) ;
  • Trinh, Thanh-Huong (Department of Architecture, College of Engineering, Nihon University) ;
  • Le, Thi-Ha (Theoretical Group, Hanoi University of Transport and Communications) ;
  • Nguyen, Dinh-Kien (Department of Solid Mechanics, Institute of Mechanics, Vietnam Academy of Science and Technology)
  • 투고 : 2014.06.11
  • 심사 : 2014.11.24
  • 발행 : 2015.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.

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과제정보

연구 과제 주관 기관 : NAFOSTED

참고문헌

  1. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration chatacteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  2. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164
  3. Fryba, L. (1972), Vibration of solids and structures under moving loads, Academia, Prahue.
  4. Geradin, M. and Rixen, D. (1997), Mechanical vibrations. Theory and application to structural dynamics, 2nd edition, John Willey & Sons, Chichester.
  5. Henchi, K., Fafard, M., Dhatt, G. and Talbot, M. (1997), "Dynamic behavior of multi-span beams under moving loads", J. Sound Vib., 199(1), 33-50. https://doi.org/10.1006/jsvi.1996.0628
  6. Huang, Y. and Li, F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform cross-section", J. Sound Vib., 96(1), 45-53. https://doi.org/10.1016/0022-460X(84)90593-5
  7. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  8. Kosmatka, J.B. (1995), "An improve two-node finite element for stability and natural frequencies of axialloaded Timoshenko beams", Comput. Struct., 57(1), 141-149. https://doi.org/10.1016/0045-7949(94)00595-T
  9. Li, S., Hu, J., Zhai, C. and Xie, L. (2013), "A unified method for modeling of axially and/or transversally functionally graded beams with variable cross-section profile", Mech. Bas. Des. Struct. Mach., 41, 168-188. https://doi.org/10.1080/15397734.2012.709466
  10. Lin, W.H. and Trethewey, M.W. (1990), "Finite element analysis of elastic beams subjected to moving dynamic loads", J. Sound Vib., 136, 323-342. https://doi.org/10.1016/0022-460X(90)90860-3
  11. Nguyen, D.K. (2008), "Dynamic response of prestressed Timoshenko beams resting on two-parameter foundation to moving harmonic load", Technische Mechanik, 28(3-4), 237-258.
  12. Nguyen, D.K. and Le, H.T. (2011), "Dynamic characteristics of elastically supported beam subjected to a compressive axial force and a moving load", Viet. J. Mech., 33(2), 113-131.
  13. Nguyen, D.K. (2013), "Large displacement response of tapered cantilever beams made of axially functionally graded material", Compos. Part B: Eng., 55, 298-305. https://doi.org/10.1016/j.compositesb.2013.06.024
  14. Nguyen, D.K., Gan, B.S. and Le, T.H. (2013), "Dynamic response of non-uniform functionally graded beams subjected to a variable speed moving load", J. Comput. Sci. Tech., JSME, 7, 12-27. https://doi.org/10.1299/jcst.7.12
  15. Nguyen, D.K. and Gan, B.S. (2014), "Large deflections of tapered functionally graded beams subjected to end loads", Appl. Math. Model., 38, 3054-3066. https://doi.org/10.1016/j.apm.2013.11.032
  16. Nguyen, D.K., Gan, B.S. and Trinh, T.H. (2014), "Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material", Struct. Eng. Mech., 49(6), 727-743. https://doi.org/10.12989/sem.2014.49.6.727
  17. Olsson, M. (1991), "On the fundamental moving load problem", J. Sound Vib., 152(2), 229-307.
  18. Shahba, A., Attarnejad, R., Marvi, T. and Hajilar, S. (2011a), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos. Part B: Eng., 42(4), 801-808. https://doi.org/10.1016/j.compositesb.2011.01.017
  19. Shahba, A., Attarnejad, R. and Hajilar, S. (2011b), "Free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams", Shock Vib., 18(5), 683-696. https://doi.org/10.1155/2011/591716
  20. Simsek, M. and Kocaturk, T. (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024
  21. Simsek, M. (2010), "Vibration analysis of a functionally graded beam under a moving mass by using different beam theories", Compos. Struct., 92(4), 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
  22. Simsek, M., Kocaturk, T. and Akbas, D. (2012), "Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load", Compos. Struct., 94, 2358-2364. https://doi.org/10.1016/j.compstruct.2012.03.020
  23. Thambiranam, D. and Zhuge, Y. (1996), "Dynamic analysis of beams on elastic foundation subjected to moving loads", J. Sound Vib., 198, 149-169. https://doi.org/10.1006/jsvi.1996.0562

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