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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)
  • 발행 : 1996.09.25

초록

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.

키워드

참고문헌

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피인용 문헌

  1. Dynamic buckling of a single-degree-of-freedom system with variable mass vol.20, pp.4, 2001, https://doi.org/10.1016/S0997-7538(01)01160-3
  2. Dynamic analysis of a cutting mechanism vol.35, pp.10, 2000, https://doi.org/10.1016/S0094-114X(00)00007-0
  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