Structural Engineering and Mechanics

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Effects of geometric parameters on in-plane vibrations of two-stepped circular beams

  • Received : 2011.07.09
  • Accepted : 2012.03.07
  • Published : 2012.04.25
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Abstract

In-plane free vibrations of circular beams with stepped cross-sections are investigated by using the exact analytical solution. The axial extension, transverse shear deformation and rotatory inertia effects are taken into account. The stepped arch is divided into a number of arches with constant cross-sections. The exact solution of the governing equations is obtained by the initial value method. Several examples of arches with different step ratios, different locations of the steps, boundary conditions, opening angles and slenderness ratios for the first few modes are presented to illustrate the validity and accuracy of the method. The effects of the geometric parameters on the natural frequencies are investigated in details. Several examples in the literature are solved and the results are given in tables. The agreement of the results is good for all examples considered. The mode transition phenomenon is also observed for the stepped arches. Some examples are solved also numerically by using the commercial finite element program ANSYS.

Keywords

References

  1. Auciello, N.M. and De Rosa, M.A. (1994), "Free vibrations of circular arches: A review", J. Sound Vib., 176(4), 433-458. https://doi.org/10.1006/jsvi.1994.1388
  2. Balasubramanian, T.S. and Prathap, G. (1989), "A field consistent higher-order curved beam element for static and dynamic analysis of stepped arches", Comput. Struct., 33, 281-288. https://doi.org/10.1016/0045-7949(89)90151-X
  3. Chidamparam, P. and Leissa, A.W. (1993), "Vibrations of a planar curved beams, rings and arches", Appl. Mech. Rev., 46, 467-483. https://doi.org/10.1115/1.3120374
  4. Dong, G.H., Hao, S.H., Zhao, Y.P., Zong, Z. and Gui, F.K. (2010a), "Numerical analysis of the flotation ring of a gravity-type fish cage", J. Offshore Mech. Arct., 132(3), 031304. https://doi.org/10.1115/1.4001416
  5. Dong, G.H., Hao, S.H., Zhao, Y.P., Zong, Z. and Gui, F.K. (2010b), "Elastic responses of a flotation ring in water waves", J. Fluid Struct., 26(1), 176-192. https://doi.org/10.1016/j.jfluidstructs.2009.09.001
  6. Gutierrez, R.H., Laura, P.A.A., Rossi, R.E., Berteo, R. and Villaggi, A. (1989), "In-plane vibrations of noncircular arches of non-uniform cross-section", J. Sound Vib., 129, 181-200. https://doi.org/10.1016/0022-460X(89)90577-4
  7. Hu, Y.J., Yang, Y.J. and Kitipornchai, S. (2010), "Pull-in analysis of electrostatically actuated curved microbeams with large deformation", Smart Mater Struct, 19, 065030. https://doi.org/10.1088/0964-1726/19/6/065030
  8. Jang, K.S., Kang, T.W., Lee, K.S., Kim, C. and Kim, T.W. (2010), "The effect of change in width on stress distribution along the curved segments of stents", J. Mech. Sci. Technol., 24(6), 1265-1271. https://doi.org/10.1007/s12206-010-0335-2
  9. Karami, G. and Malekzadeh, P. (2004), "In-plane free vibration analysis of circular arches with varying crosssections using differential quadrature method", J. Sound Vib., 274, 777-799. https://doi.org/10.1016/S0022-460X(03)00786-7
  10. Karami, M.A., Yardimoglu, B. and Inman, D.J. (2010), "Coupled out of plane vibrations of spiral beams for micro-scale applications", J. Sound Vib., 329(26), 5584-5599. https://doi.org/10.1016/j.jsv.2010.07.013
  11. Laura, P.A.A. and Maurizi, M.J. (1987), "Recent research on vibrations of arch-type structures", Shock Vib Dig, 19, 6-9.
  12. Laura, P.A.A., Verniere De Irassar, P.L., Carnicer, R. and Berteo, R. (1988), "A note on vibrations of a circumferential arch with thickness varying in a discontinuous fashion", J. Sound Vib., 120, 95-105. https://doi.org/10.1016/0022-460X(88)90336-7
  13. Lin, H.Y. (2008), "On the natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of concentrated elements", Struct. Eng. Mech., 29(5), 531-550. https://doi.org/10.12989/sem.2008.29.5.531
  14. Lin, H.Y. (2010), "An exact solution for free vibrations of a non-uniform beam carrying multiple elasticsupported rigid bars", Struct. Eng. Mech., 34(4), 399-416. https://doi.org/10.12989/sem.2010.34.4.399
  15. Liu, G.R. and Wu, T.Y. (2001), "In-plane vibration analyses of circular arches by the generalized differential quadrature rule", Int. J. Mech. Sci., 43, 2597-2611. https://doi.org/10.1016/S0020-7403(01)00052-2
  16. Lu, P., Zhao, R. and Zhang, J. (2010), "Experimental and finite element studies of special-shape arch bridge for self-balance", Struct. Eng. Mech., 35(1), 37-52. https://doi.org/10.12989/sem.2010.35.1.037
  17. Markus, S. and Nanasi, T. (1981), "Vibration of curved beams", Shock Vib. Dig., 13, 3-14.
  18. Ouakad, H.M. and Younis, M.I. (2011), "Natural frequencies and mode shapes of initially curved carbon nanotube resonators under electric excitation", J. Sound Vib., 330(13), 3182-3195. https://doi.org/10.1016/j.jsv.2010.12.029
  19. Ren, W.X., Su, C.C. and Yan, W.J. (2010), "Dynamic modeling and analysis of arch bridges using beam-arch segment assembly", CMES-Comp. Model Eng., 70(1), 67-92.
  20. Rossi, R.E., Laura, P.A.A. and Verniere De Irassar, P.L. (1989), "In-plane vibrations of cantilevered non-circular arcs of non-uniform cross-section with a tip mass", J. Sound Vib., 129, 201-213. https://doi.org/10.1016/0022-460X(89)90578-6
  21. Rossi, R.E. and Laura, P.A.A. (1995), "Numerical experiments on dynamic stiffening of a circular arch executing in-plane vibrations", J. Sound Vib., 187, 897-909. https://doi.org/10.1006/jsvi.1995.0572
  22. Tarnopolskaya, T., De Hoog, F.R., Fletcher, N.H. and Thwaites, S. (1996), "Asymptotic analysis of the free inplane vibrations of beams with arbitrarily varying curvature and cross-section", J. Sound Vib., 196, 659-680. https://doi.org/10.1006/jsvi.1996.0507
  23. Tarnopolskaya, T., De Hoog, F.R. and Fletcher, N.H. (1999), "Low-frequency mode transition in the free in-plane vibration of curved beams", J. Sound Vib., 228, 69-90. https://doi.org/10.1006/jsvi.1999.2400
  24. Tong, X., Mrad, N. and Tabarrok, B. (1998), "In-plane vibration of circular arches with variable cross-sections", J. Sound Vib., 212, 121-140. https://doi.org/10.1006/jsvi.1997.1441
  25. 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, 845-856. https://doi.org/10.1006/jsvi.1997.1290
  26. Tufekci, E. (2001), "Exact solution of free in-plane vibration of shallow circular arches", Int. J. Struct. Stab. D., 1, 409-428. https://doi.org/10.1142/S0219455401000226
  27. Tufekci, E. and Ozdemirci, O. (2006), "Exact solution of free in-plane vibration of a stepped circular arch", J. Sound Vib., 295, 725-738. https://doi.org/10.1016/j.jsv.2006.01.048
  28. Tunay, I., Yoon, S.Y., Woerner, K. and Viswanathan, R. (2009), "Vibration analysis and control of magnet positioner using curved beam models", IEEE T. Contr. Syst. T., 17(6), 1415-1423. https://doi.org/10.1109/TCST.2008.2007651
  29. Verniere De Irassar, P.L. and Laura, P.A.A. (1987), "A note on the analysis of the first symmetric mode of vibration of circular arches of non-uniform cross-section", J. Sound Vib., 116, 580-584. https://doi.org/10.1016/S0022-460X(87)81387-1
  30. Viola, E., Dilena, M. and Tornabene, F. (2007), Analytical and numerical results for vibration analysis of multistepped and multi-damaged circular arches", J. Sound Vib., 299(1-2), 143-163. https://doi.org/10.1016/j.jsv.2006.07.001
  31. Xia, W. and Wang, L. (2010), "Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape", Comp. Mater. Sci., 49, 99-103. https://doi.org/10.1016/j.commatsci.2010.04.030
  32. Younis, M.I., Ouakad, H.M., Alsaleem, F.M., Miles, R. and Cui, W. (2010), "Nonlinear dynamics of MEMS arches under harmonic electrostatic actuation", J. Microelectromech. S., 19(3), 647-656. https://doi.org/10.1109/JMEMS.2010.2046624
  33. Zhou, Y., Dong, Y. and Li, S. (2010), "Analysis of a curved beam MEMS piezoelectric vibration energy harvester", Adv. Mat. Res., 139-141, 1578-1581. https://doi.org/10.4028/www.scientific.net/AMR.139-141.1578

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