Structural Engineering and Mechanics

  • 제43권5호
  • /
  • Pages.561-582
  • /
  • 2012
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration analysis of non-prismatic beams under variable axial forces

  • Saffari, H. (Department of Civil Engineering, Shahid Bahonar University of Kerman) ;
  • Mohammadnejad, M. (Department of Civil Engineering, Birjand University of Technology) ;
  • Bagheripour, M.H. (Department of Civil Engineering, Shahid Bahonar University of Kerman)
  • 투고 : 2012.02.22
  • 심사 : 2012.08.06
  • 발행 : 2012.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

키워드

참고문헌

  1. Antes, H. (2003), "Fundamental solution and integral equations for Timoshenko beams", J. Comput. Struct., 81(6), 383-396. https://doi.org/10.1016/S0045-7949(02)00452-2
  2. Arboleda-Monsalve, L.G., Zapata-Medina, D.G. and Aristizabal-Ochoa, J.D. (2007), "Stability and natural frequencies of a weakened Timoshenko beam-column with generalized end conditions under constant axial load", J. Sound Vib., 307(1-2), 89-112. https://doi.org/10.1016/j.jsv.2007.06.059
  3. Bahadir Yuksel, S. (2012), "Assessment of non-prismatic beams having symmetrical parabolic haunches with constant haunch length ratio of 0.5", Struct. Eng. Mech., 42(6), 849-966. https://doi.org/10.12989/sem.2012.42.6.849
  4. Caruntu, D.I. (2009), "Dynamic modal characteristics of transverse vibrations of cantilevers of parabolic thickness", J. Mech. Res. Commun., 36(3), 391-404. https://doi.org/10.1016/j.mechrescom.2008.07.005
  5. Clough, R.W. and Penzien, J. (1975), Dynamics of Structures, McGraw-Hill Book Company, New York.
  6. Elfelsoufi, Z. and Azrar, L. (2005), "Buckling flutter and vibration analyses of beams by integral equation formulations", J. Comput. Struct., 83(31-32), 2632-2649. https://doi.org/10.1016/j.compstruc.2005.04.001
  7. Elfelsoufi, Z. and Azrar, L. (2006), "Integral equation formulation and analysis of the dynamic stability of damped beams subjected to subtangential follower forces", J. Sound Vib., 296(4-5), 690-713. https://doi.org/10.1016/j.jsv.2006.01.019
  8. 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(11), 2291-2303. https://doi.org/10.1016/j.jsv.2009.12.029
  9. Kaviani, P., Rahgozar, R. and Saffari, H. (2008), "Approximate analysis of tall buildings using sandwich beam models with variable cross section", Struct. Des. Tall Spec. Build., 17(2), 401-418. https://doi.org/10.1002/tal.360
  10. 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(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  11. Li, Q.S., Fang, J.Q. and Jeary, A.P. (2000), "Free vibration analysis of cantilevered tall structures under various axial loads", J. Eng. Struct., 22(5), 525-534. https://doi.org/10.1016/S0141-0296(98)00124-2
  12. Li, Q.S. (2001), "Exact solutions for buckling of non-uniform columns under axial concentrated and distributed loading", Eur. J. Mech. - A/Solids, 20(3), 485-500. https://doi.org/10.1016/S0997-7538(01)01143-3
  13. Pan, D., Chen, G. and Lou, M. (2011), "A modified modal perturbation method for vibration characteristics of non-prismatic Timoshenko beams", Struct. Eng. Mech., 40(5), 689-703. https://doi.org/10.12989/sem.2011.40.5.689
  14. Rahai, A.R. and Kazemi, S. (2008), "Buckling analysis of non-prismatic columns based on modified vibration modes", J. Commun. Nonlin. Sci. Numer. Simul., 13(8), 1721-1735. https://doi.org/10.1016/j.cnsns.2006.09.009
  15. Shooshtari, A. and Khajavi, R. (2010), "An efficient procedure to find shape functions and stiffness matrices of non-prismatic Euler-Bernoulli and Timoshenko beam elements", Eur. J. Mech. A/Solids, 29(5), 826-836. https://doi.org/10.1016/j.euromechsol.2010.04.003
  16. Yavari, A., Sarkani, S. and Reddy, J.N. (2001), "On non-uniform Euler-Bernoulli and Timoshenko beams with jump discontinuities: application of distribution theory", Int. J. Solids Struct., 38(46-47), 8389-8406. https://doi.org/10.1016/S0020-7683(01)00095-6

피인용 문헌

  1. Tailoring the second mode of Euler-Bernoulli beams: an analytical approach vol.51, pp.5, 2014, https://doi.org/10.12989/sem.2014.51.5.773
  2. A new analytical approach for determination of flexural, axial and torsional natural frequencies of beams vol.55, pp.3, 2015, https://doi.org/10.12989/sem.2015.55.3.655
  3. Stability and non-stationary vibration analysis of beams subjected to periodic axial forces using discrete singular convolution vol.44, pp.4, 2012, https://doi.org/10.12989/sem.2012.44.4.487
  4. Neuro-fuzzy and artificial neural networks modeling of uniform temperature effects of symmetric parabolic haunched beams vol.56, pp.5, 2015, https://doi.org/10.12989/sem.2015.56.5.787
  5. Performance of non-prismatic simply supported prestressed concrete beams vol.52, pp.4, 2014, https://doi.org/10.12989/sem.2014.52.4.723
  6. Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.871
  7. A new approach for free vibration analysis of nonuniform tall building structures with axial force effects pp.15417794, 2019, https://doi.org/10.1002/tal.1591
  8. Modeling for fixed-end moments of I-sections with straight haunches under concentrated load vol.23, pp.5, 2012, https://doi.org/10.12989/scs.2017.23.5.597
  9. Flapwise and non-local bending vibration of the rotating beams vol.72, pp.2, 2019, https://doi.org/10.12989/sem.2019.72.2.229
  10. Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method vol.42, pp.5, 2020, https://doi.org/10.1007/s40430-020-02332-3