Dynamic stability criteria of nonlinear elastic damped/undamped systems under step loading
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Raftoyiannis, J
(EN)
Kounadis, AN
(EN)
The nonlinear dynamic stability of simple nonlinearly elastic systems with or without viscous damping under step loading of infinite or finite duration is discussed. The analysis refers to discrete structural systems with one or two degrees of freedom which, under the action of the same loading applied statically, lose their stability by snapping. Considering the stability of motion in the large, in the sense of Lagrange, conditions for a bounded or an unbounded motion and thereby dynamic buckling criteria are properly established for one degree-of-freedom systems. It is found that, regardless of the length of time of loading application as well as regardless of whether or not damping is included, the motion ceases to be bounded when the phase-point velocity vanishes. Using this criterion, exact or approximate (lower bound) dynamic buckling loads for damped or undamped systems under step loading of infinite or finite duration can be obtained without solving the strongly nonlinear differential equation of motion.
(EN)
