Structural Engineering and Mechanics

  • 제16권2호
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  • Pages.195-217
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  • 2003
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Effect of boundary conditions on the stability of beams under conservative and non-conservative forces

  • 투고 : 2003.02.15
  • 심사 : 2003.05.26
  • 발행 : 2003.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

키워드

참고문헌

  1. Argyris, J.H. and Symeonidis, Sp. (1981), "Nonlinear finite element analysis of elastic systems under nonconservative loading-natural formulation. Part. I Quasistatic problems", Comput. Meth. Appl. Mech. Eng., 26, 75-123. https://doi.org/10.1016/0045-7825(81)90131-6
  2. Beck, M. (1952), "Die Knicklast des einseitig eingespannten, tangential gedruckten Stabes", Z. Angew. Math.Phys., 3, 225-228. https://doi.org/10.1007/BF02008828
  3. Bolotin, V.V. (1965), Non-conservative Problems of the Theory of Elastic Stability, Pergamon Press, London.
  4. De Rosa, M. and Franciosi, C. (1990), "The influence of an intermediate support on the stability behaviour ofcantilever beams subjected to follower forces", J. Sound Vib., 137(1), 107-115. https://doi.org/10.1016/0022-460X(90)90719-G
  5. Glabisz, W. (1999), "Vibration and stability of a beam with elastic supports and concentrated masses underconservative and non-conservative forces", Comput. Struct., 70, 305-313. https://doi.org/10.1016/S0045-7949(98)00181-3
  6. Kounadis, A.N. (1983), "The existence of regions of divergence instability for non-conservative systems underfollower forces", Int. J. Solids Struct., 19(8), 725-733. https://doi.org/10.1016/0020-7683(83)90067-7
  7. Lee, H.P. (1995), "Dynamic stability of a rod with an intermediate spring support subject to sub-tangentialfollower forces", Comput. Meth. Appl. Mech. Eng., 125, 141-150. https://doi.org/10.1016/0045-7825(95)00797-5
  8. Leipholz, H. (1980), Stability of Elastic Systems, Sijthoff-Noordhoff, The Netherlands.
  9. Leipholz, H. and Bhalla, K. (1977), "On the solution of the stability problems of elastic rods subjected totriangularly distributed tangential follower forces", Ingenieur-Archiv, 46, 115-124. https://doi.org/10.1007/BF00538745
  10. Liebowitz, H., Vanderveldt, H. and Harris, D.H. (1967), "Carrying capacity of notched column", Int. J. SolidsStruct., 3, 489-500. https://doi.org/10.1016/0020-7683(67)90003-0
  11. Marzani, A. and Viola, E. (2002), "Influenza dell'incastro elasticamente cedevole sulla instabilità dinamica perflutter e per divergenza di una colonna", Nota tecnica n.61 DISTART, University of Bologna, Italy.
  12. Mote, Jr. (1971), "Non-conservative stability by finite elements", J. Eng. Mech. Div., EM3, 645-656.
  13. Ryu, B.J., Sugiyama, Y., Yim, K.B. and Lee, G.S. (2000), "Dynamic stability of an elastically restrained columnsubjected to triangularly distributed sub-tangential force", Comput. Struct., 76, 611-619. https://doi.org/10.1016/S0045-7949(99)00132-7
  14. Sugiyama, Y. and Kawagoe, H. (1975), "Vibration and stability of elastic columns under the combined action ofuniformly distributed vertical and tangential forces", J. Sound Vib., 38(4), 341-355. https://doi.org/10.1016/S0022-460X(75)80051-4
  15. Sugiyama, Y. and Mladenov, K.A. (1983), "Vibration and stability of elastic columns subjected to triangularly distributed sub-tangential forces", J. Sound Vib., 88(4), 447-457. https://doi.org/10.1016/0022-460X(83)90648-X
  16. Viola, E., Nobile, L. and Marzani, A. (2002), "Boundary conditions effect on the dynamic stability of beamssubjected to triangularly distributed sub-tangential forces", Proc. of the Second Int. Conf. on Advantages inStructural Engineering and Mechanics (ASEM'02), 21-23 August 2002, Busan, Korea.
  17. Ziegler, H. (1977), Principles of Structural Stability, Birkhauser, Basel/Stuttgart.

피인용 문헌

  1. Nonconservative stability problems via generalized differential quadrature method vol.315, pp.1-2, 2008, https://doi.org/10.1016/j.jsv.2008.01.056
  2. Stability behavior and free vibration of tapered columns with elastic end restraints using the DQM method vol.4, pp.3, 2013, https://doi.org/10.1016/j.asej.2012.10.005
  3. Divergence and Flutter Instability of Damped Laminated Beams Subjected to a Triangular Distribution of Nonconservative Forces vol.14, pp.6, 2011, https://doi.org/10.1260/1369-4332.14.6.1075
  4. STABILITY OF DAMPED COLUMNS ON A WINKLER FOUNDATION UNDER SUB-TANGENTIAL FOLLOWER FORCES vol.13, pp.02, 2013, https://doi.org/10.1142/S021945541350020X
  5. Dynamic stability of shear-flexible beck’s columns based on Engesser’s and Haringx’s buckling theories vol.86, pp.21-22, 2008, https://doi.org/10.1016/j.compstruc.2008.04.012
  6. Interaction effect of cracks on flutter and divergence instabilities of cracked beams under subtangential forces vol.151, 2016, https://doi.org/10.1016/j.engfracmech.2015.11.010
  7. Stability Maps of a Cracked Timoshenko Beam Resting on Elastic Soils under Sub-Tangential Forces vol.385-387, pp.1662-9795, 2008, https://doi.org/10.4028/www.scientific.net/KEM.385-387.465