DOI QR코드

DOI QR Code

Free vibration of functionally graded thin beams made of saturated porous materials

  • Galeban, M.R. (Young Researchers and Elite Club Behbahan Branch, Islamic Azad University) ;
  • Mojahedin, A. (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University) ;
  • Taghavi, Y. (Department of Biomedical Engineering, Tehran Medical Sciences Branch, Islamic Azad University) ;
  • Jabbari, M. (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University)
  • 투고 : 2015.08.11
  • 심사 : 2016.07.04
  • 발행 : 2016.08.10

초록

This study presents free vibration of beam made of porous material. The mechanical properties of the beam is variable in the thickness direction and the beam is investigated in three situations: poro/nonlinear nonsymmetric distribution, poro/nonlinear symmetric distribution, and poro/monotonous distribution. First, the governing equations of porous beam are derived using principle of virtual work based on Euler-Bernoulli theory. Then, the effect of pores compressibility on natural frequencies of the beam is studied by considering clamped-clamped, clamped-free and hinged-hinged boundary conditions. Moreover, the results are compared with homogeneous beam with the same boundary conditions. Finally, the effects of poroelastic parameters such as pores compressibility, coefficients of porosity and mass on natural frequencies has been considered separately and simultaneously.

키워드

참고문헌

  1. Al-Ansari, L.S. (2012), "Calculating of natural frequency of stepping cantilever beam", International J. Mech. Mechatron. Eng., 12(5), 59-68.
  2. Aminbaghai, M., Murin, J. and Kuti, V. (2012), "Modal analysis of the FGM-beams with continuous transversal symmetricand longitudinal variation of material properties with effect of large axial force", Eng. Struct., 34, 314-329. https://doi.org/10.1016/j.engstruct.2011.09.022
  3. Aydin, K. (2013), "Free vibration of functionally graded beams with arbitrary number of surface cracks", Euro. J. Mech. A/Solids, 42, 112-124. https://doi.org/10.1016/j.euromechsol.2013.05.002
  4. Biot, M.A. (1964), "Theory of buckling of a porous slab and its thermoelastic analogy", J. Appl. Mech., 31(2), 194-198. https://doi.org/10.1115/1.3629586
  5. Ghassemi, A. (2007), "Stress and pore pressure distribution around a pressurized, cooled crack in low permeability rock", Proceedings of the 32nd Workshop on Geothermal Reservoir Engineering Stanford University, Stanford, CA, USA, January-February.
  6. Ghassemi, A. and Zhang, Q. (2004), "A transient fictitious stress boundary element method for porothermoelastic media", Eng. Anal. Boundary Elem., 28(11), 1363-1373. https://doi.org/10.1016/j.enganabound.2004.05.003
  7. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2014a), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140(2), 287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663
  8. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014b), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stresses, 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768
  9. Jabbari, M., Farzaneh Joubaneh, E. and Mojahedin, A. (2014c), "Thermal buckling analysis of porous circular plate with piezoelectric actuators based on first order shear deformation theory", Int. J.Mech. Sci., 83, 57-64. https://doi.org/10.1016/j.ijmecsci.2014.03.024
  10. Jabbari, M., Mojahedin, A. and Farzaneh Joubaneh, E. (2014d), "Thermal buckling analysis of circular plates made of piezoelectric and saturated porous functionally graded material layers", J. Eng. Mech., 141(4), 287-295.
  11. Jabbari, M., Mojahedin, A. and Haghi, M. (2014e), "Buckling analysis of thin circular FG plates made of saturated porous-softferro magnetic materials in transverse magnetic field", Thin-Wall. Struct., 85, 50-56. https://doi.org/10.1016/j.tws.2014.07.018
  12. Jabbari, M., Haghi, M. and Mojahedin, A. (2014f), "Buckling analysis of thin rectangular FG plates made of saturated porous-softferro magnetic materials in transverse magnetic field", J. Solid Mechanics, 85, 50-56.
  13. Jasion, P., Magnucka-Blandzi, E., Szyc, W. and Magnucki, K. (2012), "Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core", Thin-Wall. Struct., 61, 154-161. https://doi.org/10.1016/j.tws.2012.04.013
  14. Komijani, M., Esfahani, S.E., Reddy, J.N., Liu, Y.P. and Eslami, M.R. (2014), "Nonlinear thermal stability and vibration of pre/post-buckled temperature and microstructure dependent FGM beams resting on elastic foundation", Compos. Struct., 112, 297-307.
  15. Li, S.R., Cao, D.F. and Wan, Z.Q. (2013), "Bending solutions of FGM Timoshenko beams from those of the homogenous Euler-Bernoulli beams", Appl. Math. Model., 37(10-11), 7077-7085. https://doi.org/10.1016/j.apm.2013.02.047
  16. Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin-Wall. Struct., 46(3), 333-337. https://doi.org/10.1016/j.tws.2007.06.006
  17. Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47(2), 421-433.
  18. Magnucka-Blandzi, E. (2011), "Mathematical modeling of a rectangular sandwich plate with metal foam core", J. Theor. Appl. Mech., 49(2), 439-455.
  19. Magnucki, K. and Stasiewicz, P. (2004), "Elastic buckling of a porous beam", J. Theor. Appl. Mech., 42(4), 859-868.
  20. Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., Int. J., 6(4), 319-333. https://doi.org/10.12989/scs.2006.6.4.319
  21. Magnucki, K., Jasion, P., Magnucka-Blandzi, E. and Wasilewicz, P. (2014), "Theoretical and experimental study of a sandwich circular plate under pure bending", Thin-Wall. Struct., 79, 1-7. https://doi.org/10.1016/j.tws.2014.01.029
  22. Mojahedin, A., Farzaneh Joubaneh, E. and Jabbari, M. (2014), "Thermal and mechanical stability of a circular porous plate with piezoelectric actuators", Acta Mecanica., 225(12), 3437-3452. https://doi.org/10.1007/s00707-014-1153-x
  23. Murin, J., Aminbaghai, M. and Kuti, V. (2010), "Exact solution of the bending vibration problem of FGM beams with variation of material properties", Eng. Struct., 32, 1631-1640. https://doi.org/10.1016/j.engstruct.2010.02.010
  24. Murin, J., Aminbaghai, M., Hrabovsky, J., Kuti, V. and Kugler, S. (2012), "Modal analysis of the FGM beams with effect of the shear correction function", Compos.: Part B, 45, 1575-1582.
  25. Rong, L.S. and Liang, F.L. (2014), "Free vibration of FGM Timoshenko beams with through-width delamination", Sci. China Phys. Mech. Astron., 57(5), 927-934. https://doi.org/10.1007/s11433-013-5248-5
  26. Wattanasakulpong, N. and Ungbhakorn, V. (2012), "Free vibration analysis of functionally graded beams with general elastically end constraints by DTM", World J. Mech., 2(6), 297-310. https://doi.org/10.4236/wjm.2012.26036
  27. Wei, D., Liu, Y. and Xiang, Z. (2011), "An analytical method for free vibration analysis of functionally graded beams with edge cracks", J. Sound Vib., 331(7), 1686-1700. https://doi.org/10.1016/j.jsv.2011.11.020
  28. Ziane, N., Meftah, S.A., Belhadj, H.A., Tounsi, A. and Bedia, A.A. (2012), "Free vibration analysis of thin and thick-walled FGM box beams", Int. J. Mech. Sci., 66, 273-282.
  29. Zimmerman, R.W. (2000), "Coupling in poroelasticity and thermoelasticity", Int. J. Rock Mech. Mining. Sci., 37(1-2), 79-87. https://doi.org/10.1016/S1365-1609(99)00094-5

피인용 문헌

  1. Vibrations of longitudinally traveling functionally graded material plates with porosities vol.66, 2017, https://doi.org/10.1016/j.euromechsol.2017.06.006
  2. On vibrations of porous nanotubes vol.125, 2018, https://doi.org/10.1016/j.ijengsci.2017.12.009
  3. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  4. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2016, https://doi.org/10.12989/was.2018.27.1.059
  5. Free vibration of imperfect sigmoid and power law functionally graded beams vol.30, pp.6, 2019, https://doi.org/10.12989/scs.2019.30.6.603
  6. Free vibration of AFG beams with elastic end restraints vol.33, pp.3, 2016, https://doi.org/10.12989/scs.2019.33.3.403
  7. Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models vol.36, pp.3, 2016, https://doi.org/10.12989/scs.2020.36.3.293
  8. Peridynamic analysis of dynamic fracture behaviors in FGMs with different gradient directions vol.75, pp.3, 2016, https://doi.org/10.12989/sem.2020.75.3.339
  9. Axisymmetric vibration analysis of graded porous Mindlin circular plates subjected to thermal environment vol.16, pp.3, 2016, https://doi.org/10.2140/jomms.2021.16.371
  10. Quasi-3D Refined Theory for Functionally Graded Porous Plates: Vibration Analysis vol.24, pp.3, 2016, https://doi.org/10.1134/s1029959921030036
  11. A deep energy method for functionally graded porous beams vol.22, pp.6, 2016, https://doi.org/10.1631/jzus.a2000317
  12. Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition vol.40, pp.4, 2016, https://doi.org/10.12989/scs.2021.40.4.555