Structural Engineering and Mechanics

  • 제61권5호
  • /
  • Pages.685-691
  • /
  • 2017
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibrations of AFG cantilever tapered beams carrying attached masses

  • Rossit, Carlos A. (Department of Engineering, Institute of Applied Mechanics, (IMA), Universidad Nacional del Sur, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)) ;
  • Bambill, Diana V. (Department of Engineering, Institute of Applied Mechanics, (IMA), Universidad Nacional del Sur, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET)) ;
  • Gilardi, Gonzalo J. (Department of Engineering, Institute of Applied Mechanics, (IMA), Universidad Nacional del Sur, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET))
  • 투고 : 2016.07.21
  • 심사 : 2017.01.26
  • 발행 : 2017.03.10
⟨ 이전 논문 다음 논문 ⟩

초록

The free transverse vibrations of axially functionally graded (AFG) cantilever beams with concentrated masses attached at different points are studied in this paper. The material properties of the AFG beam, consisting of metal and ceramic, vary continuously in the axial direction according to an established law form. Approximated solutions for the title problem are obtained by means of the Ritz Method. The influence of the material variation on the natural frequencies of vibration of the functionally graded beam is investigated and compared with the influence of the variation of the cross section. The phenomenon of dynamic stiffening of beams can be observed in various situations. The accuracy of the procedure is verified through results available in the literature that can be represented by the model under study.

키워드

참고문헌

  1. Akgoz, B. and Civalek, O. (2013), "Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)", Compos. Part B, 55, 263-268. https://doi.org/10.1016/j.compositesb.2013.06.035
  2. Alshorbgy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35, 412-425. https://doi.org/10.1016/j.apm.2010.07.006
  3. Auciello, N.M. and Maurizi, M.J. (1997), "On the natural vibrations of tapered beams with attached inertia elements", J. Sound Vib., 199(3), 522-530. https://doi.org/10.1006/jsvi.1996.0636
  4. Bapat, C.N. and Bapat, C. (1987), "Natural Frequencies of a beam with non-classical boundary conditions and concentrated masses", J. Sound Vib., 112(1), 177-182. https://doi.org/10.1016/S0022-460X(87)80102-5
  5. Calio, I. and Elishakoff, I (2005), "Closed-form solutions for axially graded beam-columns", J. Sound Vib., 280, 1083-1094. https://doi.org/10.1016/j.jsv.2004.02.018
  6. Calio, I. and Elishakoff, I. (2004), "Closed-form trigonometric solutions for inhomogeneous beam-columns on elastic foundation", Int. J. Struct. Stab. Dyn., 4, 139-146. https://doi.org/10.1142/S0219455404001112
  7. Cetin, D. and Simsek, M. (2011), "Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler-Pasternak elastic medium", Struct. Eng. Mech., 40, 583-594. https://doi.org/10.12989/sem.2011.40.4.583
  8. Chabraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45, 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  9. Chegenizadeh, A., Ghadimi, B., Nikraz, H. and Simsek, M. (2014), "A novel two-dimensional approach to modelling functionally graded beams resting on a soil medium", Struct. Eng. Mech., 51(5), 727-741. https://doi.org/10.12989/sem.2014.51.5.727
  10. Chen, D.W. and Liu, T.L. (2006), "Free and forced vibrations of a tapered cantilever beam carrying multiple point masses", Struct. Eng. Mech., 23(2), 209-216. https://doi.org/10.12989/sem.2006.23.2.209
  11. Elishakoff, I. (2000), "A selective review of direct, semi-inverse and inverse eigenvalue problems for structures described by differential equations with variable coefficients", Arch. Comput. Meth. Eng., 7(4), 387-461. https://doi.org/10.1007/BF02736213
  12. Elishakoff, I. (2005), Eigenvalues of Inhomogeneous Structures: Unusual Closed-Form Solutions of Semi-Inverse Problems, CRC Press, Boca Raton, USA.
  13. Elishakoff, I. and Candan, S. (2001), "Apparently first closed-form solution for vibrating inhomogeneous beams", Int. J. Solid. Struct., 38(19), 3411-3441. https://doi.org/10.1016/S0020-7683(00)00266-3
  14. Elishakoff, I. and Guede, Z. (2004), "Analytical polynomial solutions for vibrating axially graded beams", Mech. Adv. Mater. Struct., 11, 517-533. https://doi.org/10.1080/15376490490452669
  15. Gan, B.S., Trinh, T.H., Le, T.H. and Nguyen, D.K. (2015), "Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads", Struct. Eng. Mech., 53(5), 981-995. https://doi.org/10.12989/sem.2015.53.5.981
  16. Hein, H. and Feklistova, L. (2011), "Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets", Eng. Struct., 33(12), 3696-3701. https://doi.org/10.1016/j.engstruct.2011.08.006
  17. Hozhabrossadat, S.M. (2015), "Exact solution for free vibration of elastically restrained cantilever non-uniform beams joined by a mass-spring system at the free end", IES J. Part A: Civil Struct. Eng., 8(4), 232-239. https://doi.org/10.1080/19373260.2015.1054957
  18. Huang, Y. and Li, X.F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform cross-section", J. Sound Vib., 329, 2291-2303. https://doi.org/10.1016/j.jsv.2009.12.029
  19. Ilanko, S. and Monterrubio, L.E. (2014), The Rayleigh-Ritz Method for Structural Analysis, John Wiley & Sons Inc., London, U.K.
  20. Karami, G., Malekzadeh, P. and Shahpari, S.A. (2003), "A DQEM for vibration of shear deformable non-uniform beams with general boundary conditions", Eng. Struct., 25, 1169-1178. https://doi.org/10.1016/S0141-0296(03)00065-8
  21. Karnovsky, I.A. and Lebed, O.I. (2004), Non-classical Vibrations of Arches and Beams, McGraw-Hill Inc., New York, USA.
  22. La Malfa, S., Laura, P.A.A., Rossit, C.A. and Alvarez, O. (2000), "Use of a dynamic absorber in the case of a vibrating printed circuit board of complicated boundary shape", J. Sound Vib., 230(3), 721-724. https://doi.org/10.1006/jsvi.1999.2579
  23. 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, 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  24. Lu, C.F. and Chen, W.Q. (2005), "Free vibration of orthotropic functionally graded beams with various end conditions", Struct. Eng. Mech., 20, 465-476. https://doi.org/10.12989/sem.2005.20.4.465
  25. Mahamood, R.M., Akinlabi, E.T., Shukla, M. and Pityana, S. (2012), "Functionally graded material: an overview", Proceedings of the World Congress on Engineering 2012, London, U.K., July.
  26. Naguleswaran, S. (2002), "Transverse vibrations of an Euler-Bernoulli uniform beam carrying several particles", Int. J. Mech. Sci., 44, 2463-2478. https://doi.org/10.1016/S0020-7403(02)00182-0
  27. Niino, M., Hirai, T. and Watanabe, R. (1987), "The functionally gradient materials", J. JPN Soc. Compos. Mater., 13, 257-264. https://doi.org/10.6089/jscm.13.257
  28. Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials", Appl. Math. Model., 36, 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073
  29. Shahba, A., Attarnejad, R., Marvi, M.T. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Compos. Part B, 42, 801-808.
  30. Simsek, M., Kocaturk, T. and Akbas, S.D. (2011), "Dynamics of an axially functionally graded beam carrying a moving harmonic load", 16th International Conference on Composite Structures, Porto, Portugal, June.
  31. Simsek, M., Kocaturk, T. and Akbas, S.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
  32. Su, H., Banerjee, J.R. and Cheung, C.W. (2013), "Dynamic stiffness formulation and free vibration analysis of functionally graded beams", Compos. Struct., 106, 854-862. https://doi.org/10.1016/j.compstruct.2013.06.029
  33. Wang, S.S. (1983), "Fracture mechanics for delamination problems in composite materials", J. Compos. Mater., 17(3), 210-223. https://doi.org/10.1177/002199838301700302
  34. Wu, J.S. and Hsieh, M. (2000), "Free vibration analysis of non-uniform beam with multiple point masses", Struct. Eng. Mech., 9(5), 449-467. https://doi.org/10.12989/sem.2000.9.5.449
  35. Wu, J.S. and Lin, T.L. (1990), "Free vibration analysis of a uniform cantilever beam with point masses by an analytical-and-numerical-combined method", J. Sound Vib., 136, 201-203. https://doi.org/10.1016/0022-460X(90)90851-P
  36. Wu, L., Wang, Q. and Elishakoff, I. (2005), "Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode", J. Sound Vib., 284, 1190-1202. https://doi.org/10.1016/j.jsv.2004.08.038

피인용 문헌

  1. A transfer matrix method for in-plane bending vibrations of tapered beams with axial force and multiple edge cracks vol.66, pp.1, 2018, https://doi.org/10.12989/sem.2018.66.1.125
  2. Timoshenko theory effect on the vibration of axially functionally graded cantilever beams carrying concentrated masses vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.703
  3. Free vibration of AFG beams with elastic end restraints vol.33, pp.3, 2017, https://doi.org/10.12989/scs.2019.33.3.403
  4. Nonlinear vibration and stability of FG nanotubes conveying fluid via nonlocal strain gradient theory vol.78, pp.1, 2021, https://doi.org/10.12989/sem.2021.78.1.103
  5. Hygro-thermal buckling of porous FG nanobeams considering surface effects vol.79, pp.3, 2021, https://doi.org/10.12989/sem.2021.79.3.359