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Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams
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 Title & Authors
Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams
Liu, Hongliang; Zhu, Xuefeng; Yang, Dixiong;
 Abstract
In-plane and out-of-plane free vibration analysis of Timoshenko curved beams is addressed based on the isogeometric method, and an effective scheme to avoid numerical locking in both of the two patterns is proposed in this paper. The isogeometric computational model takes into account the effects of shear deformation, rotary inertia and axis extensibility of curved beams, and is applicable for uniform circular beams, and more complicated variable curvature and cross-section beams as illustrated by numerical examples. Meanwhile, it is shown that, the -continuous NURBS elements remarkably have higher accuracy than the finite elements with the same number of degrees of freedom. Nevertheless, for in-plane or out-of-plane vibration analysis of Timoshenko curved beams, the NURBS-based isogeometric method also exhibits locking effect to some extent. To eliminate numerical locking, the selective reduced one-point integration and projection element based on stiffness ratio is devised to achieve locking free analysis for in-plane and out-of-plane models, respectively. The suggested integral schemes for moderately slender models obtain accurate results in both dominated and non-dominated regions of locking effect. Moreover, this strategy is effective for beam structures with different slenderness. Finally, the influence factors of structural parameters of curved beams on their natural frequency are scrutinized.
 Keywords
Timoshenko curved beams;in-plane and out-of-plane free vibration;isogeometric analysis;NURBS elements;numerical locking;
 Language
English
 Cited by
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3.
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4.
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5.
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 References
1.
Adam, C., Bouabdallah, S., Zarroug, M. and Maitournam, H. (2014), "Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams", Comput. Meth. Appl. Mech. Eng., 279, 1-28. crossref(new window)

2.
Auciello, N.M. and Rosa, M.A. (1994), "Free vibrations of circular arches: a review", J. Sound Vib., 176(4), 433-458. crossref(new window)

3.
Ball, R.E. (1967), "Dynamic analysis of rings by finite differences", ASCE J. Eng. Mech. Div., 93, 1-10.

4.
Bickford, W.B. and Strom, B.T. (1975), "Vibration of plane curved beams", J. Sound Vib., 39, 135-146. crossref(new window)

5.
Blevins, R.D. (1979), Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York, USA.

6.
Bouclier, R., Elguedj, T. and Combescure, A. (2012), "Locking free isogeometric formulations of curved thick beams", Comput. Meth. Appl. Mech. Eng., 245-246, 144-162. crossref(new window)

7.
Chidamparam, P. and Leissa, A.W. (1993), "Vibrations of planar curved beams, rings, and arches", ASME Appl. Mech. Rev., 46(9), 476-483.

8.
Cottrell, J.A., Hughes, T.J.R. and Bazilevs, Y. (2009), Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley& Sons Ltd., London, UK.

9.
Cottrell, J.A., Reali, A., Bazilevs, Y. and Hughes, T.J.R. (2006), "Isogeometric analysis of structural vibrations", Comput. Meth. Appl. Mech. Eng., 195(41-43), 5257-5296. crossref(new window)

10.
Echter, R. and Bischoff, M. (2010), "Numerical efficiency, locking and unlocking of NURBS finite elements", Comput. Meth. Appl. Mech. Eng., 199(5-8), 374-382. crossref(new window)

11.
Eisenberger, M. and Efraim, E. (2001), "In-plane vibrations of shear deformable curved beams", Int. J. Numer. Meth. Eng., 52, 1221-1234. crossref(new window)

12.
Elguedj, T., Bazilevs, Y., Calo, V.M. and Hughes, T.J.R. (2008), " B and F projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements", Comput. Meth. Appl. Mech. Eng., 197, 2732-2762. crossref(new window)

13.
Howson, W.P. and Jemah, A.K. (1999), "Exact out-of-plane natural frequencies of curved Timoshenko beams", ASCE J. Eng. Mech., 125(1), 19-25. crossref(new window)

14.
Huang, C.S., Tseng, Y.P., Chang, S.H. and Hung, C.L. (2000), "Out-of-plane dynamic analysis of beams with arbitrarily varying curvature and cross-section by dynamic stiffness matrix method", Int. J. Solid. Struct., 37(3), 495-513. crossref(new window)

15.
Huang, C.S., Tseng, Y.P., Leissa, A.W. and Nieh, K.Y. (1998), "An exact solution for in-plane vibrations of an arch having variable curvature and cross section", Int. J. Mech. Sci., 40(11), 1159-1173. crossref(new window)

16.
Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric Analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194, 4135-4195. crossref(new window)

17.
Ishaquddin, M.D., Raveendranath, P. and Reddy, J.N. (2012), "Flexure and torsion locking phenomena in out-of-plane deformation of Timoshenko curved beam element", Finite Elem. Anal. Des., 51, 22-30. crossref(new window)

18.
Ishaquddin, M.D., Raveendranath, P. and Reddy, J.N. (2013), "Coupled polynomial field approach for elimination of flexure and torsion locking phenomena in the Timoshenko and Euler-Bernoulli curved beam elements", Finite Elem. Anal. Des., 65, 17-31. crossref(new window)

19.
Kang, B., Riedel, C.H. and Tan, C.A. (2003), "Free vibration analysis of planar curved beams by wave propagation", J. Sound Vib., 260(1), 19-44. crossref(new window)

20.
Kang, K., Bert, C. and Striz, H. (1995), "Vibration analysis of shear deformation circular arches by the differential quadrature method", J. Sound Vib., 181(2), 353-360.

21.
Kim, B.Y., Kim, C.B., Song, S.G. and Beom, H.G. and Cho C.D. (2009), "A finite thin circular beam element for out-of-plane vibration analysis of curved beams", J. Mech. Sci. Tech., 23(5), 1396-1405. crossref(new window)

22.
Kim, H.J., Seo, Y.D. and Youn, S.K. (2009), "Isogeometric analysis for trimmed CAD surfaces", Comput. Meth. Appl. Mech. Eng., 198(37-40), 2982-2995. crossref(new window)

23.
Lee, B.K., Oh, S.J., Mo, J.M. and Lee, T.E. (2008), "Out-of-plane free vibrations of curved beams with variable curvature", J. Sound Vib., 318(1/2), 227-246. crossref(new window)

24.
Lee, J. and Schultz, W.W. (2004), "Eigenvalue analysis of Timoshenko beams and axisymmetric Mindlin plates by the pseudospectral method", J. Sound Vib., 269, 609-621. crossref(new window)

25.
Lee, S.J. and Park, K.S. (2013), "Vibrations of Timoshenko beams with isogeometric approach", Appl. Math. Model., 37(22), 9174-9190. crossref(new window)

26.
Luu, A.T., Kim, N.I. and Lee, J. (2015), "Isogeometric vibration analysis of free-form Timoshenko curved beams", Meccanica, 50(1), 169-187. crossref(new window)

27.
Mochida, Y. and Ilanko, S. (2016), "Condensation of independent variables in free vibration analysis of curved beams", Adv. Aircraft Spacecraft Sci., 3(1), 45-59. crossref(new window)

28.
Oh, S.J., Lee, B.K. and Lee, I.W. (1999), "Natural frequencies of non-circular arches with rotatory inertia and shear deformation", J. Sound Vib., 219(1), 23-33. crossref(new window)

29.
Piegl, L. and Tiller, W. (1997), The NURBS Book, 2nd Edition, Springer-Verlag, New York, USA.

30.
Raveendranath, P., Gajbir, S.G. and Venkateswara, R. (2001), "A three-noded shear-flexible curved beam element based on coupled displacement field interpolations", Int. J. Numer. Meth. Eng., 51, 85-101. crossref(new window)

31.
Tufekci, E. and Arpaci, A. (1998), "Exact solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects", J. Sound Vib., 209(5), 845-856. crossref(new window)

32.
Tufekci, E., Dogruer, O.Y. (2006), "Out-of-plane free vibration of a circular arch with uniform cross-section: Exact solution", J. Sound Vib., 291, 525-538. crossref(new window)

33.
Wang, D.D. and Zhang, H.J. (2014), "A consistently coupled isogeometric-meshfree method", Comput. Meth. Appl. Mech. Eng., 268, 843-870. crossref(new window)

34.
Wang, D.D., Liu, W. and Zhang, H.J. (2013), "Novel higher order mass matrices for isogeometric structural vibration analysis", Comput. Meth. Appl. Mech. Eng., 260, 92-108. crossref(new window)

35.
Wang, D.D., Liu, W. and Zhang, H.J. (2015), "Superconvergent isogeometric free vibration analysis of Euler-Bernoulli beams and Kirchhoff plates with new higher order mass matrices", Comput. Meth. Appl. Mech. Eng., 286, 230-267. crossref(new window)

36.
Weeger, O., Wever, U. and Simeon B. (2013), "Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations", Nonlin. Dyn., 72(4), 813-835. crossref(new window)

37.
Wu, J.S. and Chiang, L.K. (2003), "Free vibration analysis of arches using curved beam elements", Int. J. Numer. Meth. Eng., 58, 1907-1936. crossref(new window)

38.
Yang, F., Sedaghati, R. and Esmailzadeh, E. (2008), "Free in-plane vibration of general curved beams using finite element method", J. Sound Vib., 318(4-5), 850-867. crossref(new window)

39.
Ye, K.S. and Zhao, X.J. (2012), "Dynamic stiffness method for out-of-plane free vibration analysis of planar curved beams", Eng. Mech., 29(3), 1-8.