Structural Engineering and Mechanics

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Static and dynamic stability of a single-degree-of-freedom autonomous system with distinct critical points

  • Sophianopoulos, D.S. (Metal Structures Lab., Civil Engineering Department, National Technical University)
  • Published : 1996.09.25
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Abstract

The dynamic buckling mechanism of a single-degree-of-freedom dissipative/nondissipative gradient system is thoroughly studied, employing energy criteria. The model is chosen in such a manner, that its corresponding static response is associated with all types of distinct critical points. Under a suddenly applied load of infinite duration, it is found that dynamic buckling, occurring always through a saddle, leads to an escaped motion, which is finally attracted by remote stable equilibrium positions, belonging sometimes also to complementary paths. Moreover, although the existence of initial imperfection changes the static behaviour of the system from limit point instability to bifurcation, it is established that the proposed model is dynamically stable in the large, regardless of the values of all other parameters involved.

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References

  1. Augusti, G. (1994), "Stabilita di strutture elastiche elemenari in presenza di grandi spostamenti", Atti dell Acad. delle Sci. fis. e mat. di Napoli, 4, 5.
  2. Augusti, G. (1964), Some Problems in Structural Instability, PhD Thesis, Cambridge University.
  3. Gioncu, V. and Ivan, M. (1984), Theory of Critical and Postcritical Behavior of Elastic Structures, Editura Academiei Republicii Socialiste Romania.
  4. Kounadis, A. N. (1991), "Nonlinear dynamic buckling of discrete dissipative or nondissipative systems under step loading", AIAA J., 29(2), 280-289. https://doi.org/10.2514/3.10575
  5. Kounadis, A. N. (1993), "Static and dynamic, local and global bifurcations in nonlinear autonomous structural systems, AIAA J., 31(8), 1468-1477. https://doi.org/10.2514/3.11797
  6. Kounadis, A. N. (1994), "Nonlinear dynamic buckling and stability of autonomous dissipative discrete structural systems", CISM Course on Nonlinear Stability of Structures, Udine, Italy, September 6-10. Lecture Notes by Springer Verlag.
  7. Kounadis, A. N. and Sophianopoulos, D.S. (1995), "On the dynamic buckling mechanism of single-degree-of-freedom dissipative/nondissipative structural systems", J. of Sound and Vibration (to appear).
  8. Thompson, J.M.T. (1965), "Discrete branching points in the general theory of elastic stability", J. Mech. Phys. Solids, 15, 311.
  9. Zanaboni, O. (1962), "Carateri della instabilita elastico di la specie", G. Genio Civ., 9, 510.

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  3. Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach vol.03, pp.01, 2013, https://doi.org/10.4236/wjm.2013.31005
  4. Estimating the Region of Attraction via collocation for autonomous nonlinear systems vol.41, pp.2, 1996, https://doi.org/10.12989/sem.2012.41.2.263