Active and Passive Specific Loads with Respect to the Stability and Free Vibrations of Columns
Publication: Journal of Engineering Mechanics
Volume 140, Issue 1
Abstract
A geometrically linear slender system subjected to an active and passive specific load is discussed. The boundary conditions, which take into account the specific load, were derived on the basis of the boundary conditions for the general load (the load present at the ends of the column induced by a longitudinal and transversal force, as well as by the concentrated moment). The boundary value problem of the basic system (the system subjected to a generalized load) was formulated using Hamilton’s principle. With regard to the specific load, the column was investigated for two types of active load: a generalized load by a force directed toward the positive pole, and a load by the follower force with a circular contour directed toward the positive pole. Heads consisting of linear elements were used to realize the active load, whereas heads consisting of circular elements were used to realize the passive load by the follower force directed toward the positive pole. Numerical research concerning the critical load and characteristic curves was carried out for different values of the parameters of the considered columns. The accuracy of the assumed mathematical model is confirmed by experimental research.
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Acknowledgments
The study was carried out within the statutory funds of the Czestochowa University of Technology (BS-1-101-302/99/P) and Research Project No. N N501 117236 awarded by the Ministry of Science and Higher Education, Warsaw, Poland.
References
Aristizabal-Ochoa, J. D. (1994). “K-factor for columns in any type of construction: Nonparadoxical approach.” J. Struct. Eng., 120(4), 1272–1290.
Aristizabal-Ochoa, J. D. (2005). “Static stability of beam-columns under combined conservative and nonconservative end forces: Effects of semirigid connections.” J. Eng. Mech., 131(5), 473–484.
Awrejcewicz, J., Andrianov, I. V., and Manevitch, L. I. (2004a). Asymptotical mechanics of thin walled structures: A handbook, Springer, Berlin.
Awrejcewicz, J., Krysko, V. A., and Narkaitis, G. G. (2003). “Bifurcations of a thin plate-strip excited transversally and axially.” Nonlinear Dyn., 32(2), 187–209.
Awrejcewicz, J., Krysko, V. A., and Vakakis, A. F. (2004b). Nonlinear dynamics of continuous elastic systems, Springer, Berlin.
Awrejcewicz, J., Saltykova, O. A., Zhigalov, M. V., Hagedorn, P., and Krysko, V. A. (2011). “Analysis of non-linear vibrations of single-layered Euler-Bernoulli beams using wavelets.” Int. J. Aerosp. Lightweight Struct., 1(2), 203–219.
Beck, M. (1952). “Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes.” J. Appl. Math. Mech., 3(3), 225–228.
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(1), 88–98.
Gajewski, A. (2001). “Vibration and stability of a non-prismatic column compressed by non-conservative forces in non-linear creep conditions.” J. Sound Vibrat., 248(2), 315–327.
Gajewski, A., and Życzkowski, M. (1970). “Optimal design of elastic columns subject to the general conservative behaviour of loading.” J. Appl. Math. Phys., 21(5), 806–818.
Hernández-Urrea, J. A., and Aristizábal-Ochoa, J. D. (2008). “Static and dynamic stability of an elastically restrained Beck column with an attached end mass.” J. Sound Vib., 312(4–5), 789–800.
Kasprzycki, A. (2007). “Technical description of structures of loading columns.” Free vibrations and stability of slender objects as linear or nonlinear systems, Scientific-Technical Publishing House, Warsaw, Poland, 47–60 (in Polish).
Kounadis, A. N. (1977). “Stability of elastically restrained Timoshenko cantilevers with attached masses subjected to a follower force.” J. Appl. Mech., 44(4), 731–736.
Kounadis, A. N. (1981). “Divergence and flutter instability of elastically restrained structures under follower forces.” Int. J. Eng. Sci., 19(4), 553–562.
Kounadis, A. N. (1983). “The existence of regions of divergence instability for nonconservative systems under follower forces.” Int. J. Solids Struct., 19(8), 725–733.
Langthjem, M. A., and Sugiyama, Y. (2000). “Dynamic stability of columns subjected to follower loads: A survey.” J. Sound Vib., 238(5), 809–851.
Leipholz, H., and Piche, R. (1984). “Stability of follower-force rods with weight.” J. Eng. Mech. Div., 110(3), 367–379.
Leipholz, H. H. E. (1974). “On conservative elastic systems of the first and second kind.” Arch. Appl. Mech., 43(5), 255–271.
Pedersen, P. (1977). “Influence of boundary conditions on the stability of a column under non-conservative load.” Int. J. Solids Struct., 13(5), 445–455.
Przybylski, J. (2000). “The role of prestressing in establishing regions of instability for a compound column under conservative or nonconservative load.” J. Sound Vib., 231(2), 291–305.
Ryu, J. B., Sugiyama, Y., Yim, K. B., and Lee, G. S. (2000). “Dynamic stability of an elastically restrained column subjected to triangulary distributed subtangential forces.” Comp. Struct., 76(5), 611–619.
Sato, K. (1996). “Instability of a clamped-elastically restrained Timoshenko column carrying a tip load, subjected to a follower force.” J. Sound Vib., 194(4), 623–630.
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.
Sundararajan, C. (1976). “Influence of an elastic end support on the vibration and stability of Beck’s column.” Int. J. Mech. Sci., 18(5), 239–241.
Tomski, L., Przybylski, J., Gołębiowska-Rozanow, M., and Szmidla, J. (1998). “Vibration and stability of a cantilever column subject to a follower force passing through a fixed point.” J. Sound Vib., 214(1), 67–81.
Tomski, L., Szmidla, J., and Uzny, S. (2007). “The local and global instability and vibration of systems subjected to non-conservative loading.” Thin Walled Struct., 45, 945–949.
Tomski, L., and Uzny, S. (2008a). “Free vibration and the stability of a geometrically non-linear column loaded by a follower force directed towards the positive pole.” Int. J. Solids Struct., 45(1), 87–112.
Tomski, L., and Uzny, S. (2008b). “Vibration and stability of geometrically non-linear column subjected to generalised load by a force directed towards the positive pole.” Int. J. Struct. Stab. Dyn., 8(1), 1–24.
Tomski, L., and Uzny, S. (2011). “The regions of flutter and divergence instability of a column subjected to Beck’s generalized load taking into account the torsional flexibility of the loaded end of the column.” Mech. Res. Commun., 38(2), 95–100.
Tomski, L., and Uzny, S. (2012). “Free vibrations and stability of a new slender system subjected to a conservative or non-conservative load.” J. Eng. Mech., 139(8), 1133–1148.
Uzny, S. (2011). “Free vibrations of an elastically supported geometrically nonlinear column subjected to a generalized load with a force directed toward the positive pole.” J. Eng. Mech., 137(11), 740–748.
Wallwrestein, D. V. (2002). A variational approach to structural analysis, Wiley, New York.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 1 • January 2014
Pages: 193 - 205
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Nov 28, 2012
Accepted: Mar 28, 2013
Published online: Apr 3, 2013
Published in print: Jan 1, 2014
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