Structural Engineering and Mechanics

  • 제33권6호
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  • Pages.709-724
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  • 2009
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Effects of damping on the linear stability of a free-free beam subjected to follower and transversal forces

  • Kavianipour, O. (Department of Aerospace Engineering, K. N. T. University of Technology) ;
  • Sadati, S.H. (Department of Mechanical Engineering, K. N. T. University of Technology)
  • 투고 : 2009.04.29
  • 심사 : 2009.09.29
  • 발행 : 2009.12.20
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper a free-free uniform beam with damping effects subjected to follower and transversal forces at its end is considered as a model for a space structure. The effect of damping on the stability of the system is first investigated and the effects of the follower and transversal forces on the vibration of the beam are shown next. Proportional damping model is used in this work, hence, the effects of both internal (material) and external (viscous fluid) damping on the system are noted. In order to derive the frequency of the system, the Ritz method has been used. The mode shapes of the system must therefore be extracted. The Newmark method is utilized in the study of the system vibration. The results show that an increase in the follower and transversal forces leads to an increase of the vibrational motion of the beam which is not desirable.

키워드

참고문헌

  1. Attard, M.M., Lee, J.S. and Kim, M.Y. (2008), "Dynamic stability of shear-flexible beck's columns based on Engesser's and Haringx's buckling theories", Comput. Struct., 86(21-22), 2042-2055 https://doi.org/10.1016/j.compstruc.2008.04.012
  2. Au, F.T.K., Zheng, D.Y. and Cheung, Y.K. (1999), "Vibration and stability of non-uniform beams with abrupt changes of cross-section by using C1 modified beam vibration functions", Appl. Math. Model., 29, 19-34 https://doi.org/10.1016/j.apm.2004.07.006
  3. Beal, T.R. (1965), "Dynamic stability of a flexible missile under constant and pulsating thrusts", AIAA J., 3(3), 486-494 https://doi.org/10.2514/3.2891
  4. Bokaian, A. (1988), "Natural frequencies of beam under compressive axial loads", J. Sound Vib., 126(1), 49-65 https://doi.org/10.1016/0022-460X(88)90397-5
  5. Craig, Jr., R.R. and Kurdila, A.J. (2006), Fundamentals of Structural Dynamics, John Wiley & Sons, Inc., New Jersey
  6. De Rosa, M.A., Auciello, N.M. and Lippiello, M. (2008), "Dynamic stability analysis and DQM for beams with variable cross-section", Mech. Res. Commun., 35, 187-192 https://doi.org/10.1016/j.mechrescom.2007.10.010
  7. Detinko, F.M. (2002), "Some phenomena for lateral flutter of beams under follower load", Int. J. Solids Struct., 39, 341-350 https://doi.org/10.1016/S0020-7683(01)00202-5
  8. Detinko, F.M. (2003), "Lumped damping and stability of Beck column with a tip mass", Int. J. Solids Struct., 40, 4479-4486 https://doi.org/10.1016/S0020-7683(03)00298-1
  9. Di Egidio, A., Luongo, A. and Paolone, A. (2007) "Linear and non-linear interactions between static and dynamic bifurcations of damped planar beams", Int. J. Non-linear Mech., 42, 88-98 https://doi.org/10.1016/j.ijnonlinmec.2006.12.010
  10. Djondjorov, P.A. and Vassilev, V.M. (2008), "On the dynamic stability of a cantilever under tangential follower force according to Timoshenko beam theory", J. Sound Vib., 311, 1431-1437 https://doi.org/10.1016/j.jsv.2007.10.005
  11. 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, 690-713 https://doi.org/10.1016/j.jsv.2006.01.019
  12. Hassanpour, P.A., Cleghorn, W.L., Mills, J.K. and Esmailzadeh, E. (2007), "Exact solution of the oscillatory behavior under axial force of a beam with a concentrated mass within its interval", J. Vib. Control, 13(12), 1723-1739 https://doi.org/10.1177/1077546307076285
  13. Hodges, D.H. and Pierce, G.A. (2002), Introduction to Structural Dynamics and Aeroelasticity, The Press Syndicate of the University of Cambridge, Cambridge
  14. Joshi, A. (1995), "Free vibration characteristics of variable mass rocket having large axial thrust/acceleration", J. Sound Vib., 187(4), 727-736 https://doi.org/10.1006/jsvi.1995.0559
  15. Katsikadelis, J.T. and Tsiatas, G.C. (2007), "Optimum design of structures subjected to follower forces", Int. J. Mech. Sci., 49, 1204-1212 https://doi.org/10.1016/j.ijmecsci.2007.03.011
  16. Katsikadelis, J.T. and Tsiatas, G.C. (2007), "Nonlinear dynamic stability of damped Beck's column with variable cross-section", Int. J. Non-linear Mech., 42(1), 164-171 https://doi.org/10.1016/j.ijnonlinmec.2006.10.019
  17. Kim, J.H. and Choo, Y.S. (1998), "Dynamic stability of a free-free Timoshenko beam subjected to a pulsating follower force", J. Sound Vib., 216(4), 623-636 https://doi.org/10.1006/jsvi.1998.1717
  18. Kurnik, W. and Przyby owicz, P.M. (2003), "Active stabilisation of a piezoelectric fiber composite shaft subject to follower load", Int. J. Solids Struct., 40, 5063-5079 https://doi.org/10.1016/S0020-7683(03)00255-5
  19. Langthjem, M.A. and Sugiyama, Y. (1999), "Optimum shape design against flutter of a cantilevered column with an end-mass of finite size subjected to a non-conservative load", J. Sound Vib., 226(1), 1-23 https://doi.org/10.1006/jsvi.1999.2211
  20. Langthjem, M.A. and Sugiyama, Y. (2000), "Dynamic stability of columns subjected to follower loads: A survey", J. Sound Vib., 238, 809-851 https://doi.org/10.1006/jsvi.2000.3137
  21. Lee, H.P. (1995), "Divergence and flutter of a cantilever rod with an intermediate spring support", Int. J. Solids Struct., 32(10), 1371-1382 https://doi.org/10.1016/0020-7683(94)00205-B
  22. Lee, J.S., Kim, N.I. and Kim, M.Y. (2007), "Sub-tangentially loaded and damped Beck's columns on twoparameter elastic foundation", J. Sound Vib., 306, 766-789 https://doi.org/10.1016/j.jsv.2007.06.017
  23. Luongo, A. and Di Egidio, A. (2006), "Divergence, Hopf and double-zero bifurcations of a nonlinear planar beam", Comput. Struct., 84, 1596-1605 https://doi.org/10.1016/j.compstruc.2006.01.004
  24. Marzani, A., Tornabene, F. and Viola, E. (2008), "Nonconservative stability problems via generalized differential quadrature method", J. Sound Vib., 315, 176-196 https://doi.org/10.1016/j.jsv.2008.01.056
  25. Meirovitch, L. (1997), Principles and Techniques of Vibrations, Prentice-Hall International, Inc., New Jersey
  26. Mladenov, K.A. and Sugiyama, Y. (1997), "Stability of a jointed free-free beam under end rocket thrust", J. Sound Vib., 199(1), 1-15 https://doi.org/10.1006/jsvi.1996.0625
  27. Nihous, G.C. (1997), "On the continuity of boundary value problem for vibrating free-free straight beams under axial loads", J. Sound Vib., 200(1), 110-119 https://doi.org/10.1006/jsvi.1996.0642
  28. Paolone, A., Vastab, M. and Luongoc, A. (2006), "Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I. Non-linear model and stability analysis", Int. J. Non-Linear Mech., 41, 586-594 https://doi.org/10.1016/j.ijnonlinmec.2006.02.006
  29. Park, Y.P. and Mote, Jr., C.D. (1984), "The maximum controlled follower force on a free-free beam carrying a concentrated mass", J. Sound Vib., 98(2), 247-256 https://doi.org/10.1016/0022-460X(85)90388-8
  30. Park, Y.P. (1987), "Dynamic stability of a free Timoshenko beam under a controlled follower force", J. Sound Vib., 113(3), 407-415 https://doi.org/10.1016/S0022-460X(87)80129-3
  31. Pourtakdoust, S.H. and Assadian, N. (2004), "Investigation of thrust effect on the vibrational characteristics of flexible guided missiles", J. Sound Vib., 272, 287-299 https://doi.org/10.1016/S0022-460X(03)00779-X
  32. Ravi Kumar, L., Datta, P.K. and Prabhakara, D.L. (2005), "Dynamic instability characteristics of laminated composite doubly curved panels subjected to partially distributed follower edge loading", Int. J. Solids Struct., 42, 2243-2264 https://doi.org/10.1016/j.ijsolstr.2004.09.024
  33. Ryu, S.U. and Sugiyama, Y. (2003), "Computational dynamics approach to the effect of damping on stability of a cantilevered column subjected to a follower force", Comput. Struct., 81, 265-271 https://doi.org/10.1016/S0045-7949(02)00436-4
  34. Sato, K. (1991), "On the governing equation for vibrating and stability of a Timoshenko beam: Hamilton's Principle", J. Sound Vib., 145(2), 338-340 https://doi.org/10.1016/0022-460X(91)90597-D
  35. Shvartsman, B.S. (2007), "Large deflections of a cantilever beam subjected to a follower force", J. Sound Vib., 304, 969-973 https://doi.org/10.1016/j.jsv.2007.03.010
  36. Sugiyama, Y. and Langthjem, M.A. (2007), "Physical mechanism of the destabilizing effect of damping in continuous non-conservative dissipative systems", Int. J. Non-Linear Mech., 42(1), 132-145 https://doi.org/10.1016/j.ijnonlinmec.2006.11.011
  37. Thana, H.K. and Ameen, M. (2007), "Finite element analysis of dynamic stability of skeletal structures under periodic loading", J. Zhejiang University Science A, 8(2), 245-256 https://doi.org/10.1631/jzus.2007.A0245
  38. Tomski, L., Szmidla, J. and Uzny, S. (2007), "The local and global instability and vibration of systems subjected to non-conservative loading", Thin Wall. Struct., 45, 945-949 https://doi.org/10.1016/j.tws.2007.08.019
  39. Tsiatas, G.C. and Katsikadelis, J.T. (2009), "Post-critical behavior of damped beam columns with variable crosssection subjected to distributed follower forces", Nonlinear Dynam., 56(4), 429-441 https://doi.org/10.1007/s11071-008-9412-9
  40. Wang, Q. and Quek, S.T. (2002), "Enhancing flutter and buckling capacity of column by piezoelectric layers", Int. J. Solids Struct., 39, 4167-4180 https://doi.org/10.1016/S0020-7683(02)00334-7
  41. Wang, Q. (2004), "A comprehensive stability analysis of a cracked beam subjected to follower compression", Int. J. Solids Struct., 41, 4875-4888 https://doi.org/10.1016/j.ijsolstr.2004.04.037
  42. Wu, J.J. (1975), "On the stability of a free-free beam under axial thrust subjected to directional control", J. Sound Vib., 43(1), 45-52 https://doi.org/10.1016/0022-460X(75)90203-5
  43. Young, T.H. and Juan, C.S. (2003), "Dynamic stability and response of fluttered beams subjected to random follower forces", Int. J. Non-Linear Mech., 38, 889-901 https://doi.org/10.1016/S0020-7462(02)00035-5
  44. Zuo, Q.H. and Schreyer, H.L. (1996), "Flutter and divergence instability of nonconservative beams and plates", Int. J. Solids Struct., 33(9), 1355-1367 https://doi.org/10.1016/0020-7683(95)00097-6

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