Structural Engineering and Mechanics

  • 제32권6호
  • /
  • Pages.811-833
  • /
  • 2009
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analyses of tapered fgm beams with nonlocal theory

  • Pradhan, S.C. (Department of Aerospace Engineering, Indian Institute of Technology Kharagpur) ;
  • Sarkar, A. (Department of Aerospace Engineering, Indian Institute of Technology Kharagpur)
  • 투고 : 2008.09.03
  • 심사 : 2009.07.09
  • 발행 : 2009.08.20
⟨ 이전 논문 다음 논문 ⟩

초록

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

키워드

참고문헌

  1. Brown, R.E. and Stone, M.A. (1997), "On the use of polynomial series with the RR method", Compos. Struct., 39(3-4), 191-196 https://doi.org/10.1016/S0263-8223(97)00113-X
  2. Ece, M.C., Aydogdu, M. and Taskin, V. (2007), "Vibration of a variable cross-section beam", Mech. Res. Commun., 34(1), 78-84 https://doi.org/10.1016/j.mechrescom.2006.06.005
  3. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16 https://doi.org/10.1016/0020-7225(72)90070-5
  4. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phy., 54, 4703-4710 https://doi.org/10.1063/1.332803
  5. Eringen, A.C. (2002), Nonlocal Continuum Field Theories, Springer-Verlag, New York
  6. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248 https://doi.org/10.1016/0020-7225(72)90039-0
  7. Ganesan, R. and Zabihollah, A. (2007b), "Vibration analysis of tapered composite beams using a higher-order finite element. Part II: Parametric study", Compos. Struct., 77, 319-330 https://doi.org/10.1016/j.compstruct.2005.07.017
  8. Ganesan, R. and Zabihollah, A. (2007a), "Vibration analysis of tapered composite beams using a higher-order finite element. Part I: Parametric study", Compos. Struct., 77, 306-318 https://doi.org/10.1016/j.compstruct.2005.07.018
  9. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound wave propagation in single-walled carbon nanotubes using nonlocal elasticity", Physica E: Low-dimensional Systems and Nanostructures, (in press)
  10. Leissa, A.W. (2005), "The historical bases of RR methods", J. Sound Vib., 287, 961-978
  11. Liew,. K.M., Wang, J., Ng, T.Y. and Tan, M.J. (2004), "Free vibration and buckling analysis of sheardeformable plates based on FSDT meshfree method", J. Sound Vib., 276, 997-1017 https://doi.org/10.1016/j.jsv.2003.08.026
  12. Maalek, S. (2004), "Shear deflections of tapered timoshenko beams", Int. J. Mech. Sci., 46, 783-805 https://doi.org/10.1016/j.ijmecsci.2004.05.003
  13. Murmu, T. and Pradhan, S.C. (2008), "Buckling analysis of beam on winkler foundation by using MDQM and nonlocal theory", J. Aerospace Sci. Technol., 60(3), 206-215
  14. Peddieson, J., Buchanan, G.G. and McNitt, R.P. (2003) "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312 https://doi.org/10.1016/S0020-7225(02)00210-0
  15. Pin, L., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct., 44(16), 5289-5300 https://doi.org/10.1016/j.ijsolstr.2006.12.034
  16. Pradhan, S.C. (2005), "Vibration suppression of FGM composite shells using embedded magnetostrictive layers", Int. J. Solids Struct., 42(9-10), 2465-2488 https://doi.org/10.1016/j.ijsolstr.2004.09.049
  17. Pradhan, S.C. (2008), "Thermal buckling of functionally graded plates with cutouts", J. Aerospace Sci. Technol., 60(1), 60-76
  18. Pradhan, S.C., Loy, C.T., Lam, K.Y. and Reddy, J.N. (2000), "Vibration characteristics of functionally graded cylindrical shells under various boundary conditions", Appl. Acoust., 61(1), 111-129 https://doi.org/10.1016/S0003-682X(99)00063-8
  19. Reddy, J.N. (2007), "Non-local theories for bending, buckling and vibration of beams", Int. J. Eng. Sci., 45, 288-307 https://doi.org/10.1016/j.ijengsci.2007.04.004
  20. Reddy, J.N. and Wang, C.M. (2000), "An overview of the relationship between solutions of the classical and shear deformation plate theories", Compos. Sci. Tech., 60, 2327-2335 https://doi.org/10.1016/S0266-3538(00)00028-2
  21. Reddy, J.N., Wang, C.M. and Lee, K.H. (1997), "Relationship between bending solutions of classical and shear deformation beam theories", Int. J. Solids Struct., 34(26), 3373-3384 https://doi.org/10.1016/S0020-7683(96)00211-9
  22. Shames, I. and Dym, C.L. (2006), Energy and Finite Element Methods in Structural Mechanics, New age International Publication. New Delhi, India
  23. Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures", Phys. Lett. A, 363(3), 236-242 https://doi.org/10.1016/j.physleta.2006.10.093
  24. Zhou, D. and Chung, Y.K. (2000), "The free vibration of tapered beams", Comput. Meth. Appl. Mech. Eng., 188, 203-216 https://doi.org/10.1016/S0045-7825(99)00148-6

피인용 문헌

  1. Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM vol.50, pp.3, 2011, https://doi.org/10.1016/j.commatsci.2010.11.001
  2. Surface Elasticity Effects Can Apparently Be Explained Via Their Nonconservativeness vol.2, pp.3, 2011, https://doi.org/10.1115/1.4005486
  3. Nonlinear cylindrical bending analysis of E-FGM plates with variable thickness vol.16, pp.4, 2014, https://doi.org/10.12989/scs.2014.16.4.339
  4. Mechanical Buckling Analysis of Single-Walled Carbon Nanotube with Nonlocal Effects vol.48, 2017, https://doi.org/10.4028/www.scientific.net/JNanoR.48.85
  5. Surface effects on axial buckling of nonuniform nanowires using non-local elasticity theory vol.6, pp.1, 2011, https://doi.org/10.1049/mnl.2010.0191
  6. Buckling analysis and small scale effect of biaxially compressed graphene sheets using non-local elasticity theory vol.37, pp.4, 2012, https://doi.org/10.1007/s12046-012-0088-y
  7. Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load vol.94, pp.8, 2012, https://doi.org/10.1016/j.compstruct.2012.03.020
  8. Analysis of axially functionally graded nano-tapered Timoshenko beams by element-based Bernstein pseudospectral collocation (EBBPC) 2017, https://doi.org/10.1007/s00366-017-0557-3
  9. A unified formulation for static behavior of nonlocal curved beams vol.59, pp.3, 2016, https://doi.org/10.12989/sem.2016.59.3.475
  10. Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method vol.59, pp.1, 2016, https://doi.org/10.12989/sem.2016.59.1.001
  11. Forced vibration of an embedded single-walled carbon nanotube traversed by a moving load using nonlocal Timoshenko beam theory vol.11, pp.1, 2011, https://doi.org/10.12989/scs.2011.11.1.059
  12. Axial vibration of carbon nanotube heterojunctions using nonlocal elasticity vol.49, pp.3, 2010, https://doi.org/10.1016/j.commatsci.2010.06.003
  13. Thermo mechanical buckling analysis of carbon nanotubes on winkler foundation using non-local elasticity theory and DTM vol.36, pp.6, 2011, https://doi.org/10.1007/s12046-011-0052-2
  14. Finite element static and dynamic analysis of axially functionally graded nonuniform small-scale beams based on nonlocal strain gradient theory pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1432797
  15. Measuring material length parameter with a new solution of microbend beam in couple stress elasto-plasticity vol.33, pp.2, 2009, https://doi.org/10.12989/sem.2009.33.2.257
  16. Mathematical solution for free vibration of sigmoid functionally graded beams with varying cross-section vol.11, pp.6, 2009, https://doi.org/10.12989/scs.2011.11.6.489
  17. Free vibration of an axially functionally graded pile with pinned ends embedded in Winkler-Pasternak elastic medium vol.40, pp.4, 2009, https://doi.org/10.12989/sem.2011.40.4.583
  18. Lateral-Torsional Stability Analysis of a Simply Supported Axially Functionally Graded Beam with a Tapered I-Section vol.56, pp.1, 2009, https://doi.org/10.1007/s11029-020-09859-5
  19. Large amplitude free torsional vibration analysis of size-dependent circular nanobars using elliptic functions vol.77, pp.4, 2021, https://doi.org/10.12989/sem.2021.77.4.535