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Noise-Induced Snap-Through of a Buckled Column With Continuously Distributed Mass: A Chaotic Dynamics Approach.


pdf icon Noise-Induced Snap-Through of a Buckled Column With Continuously Distributed Mass: A Chaotic Dynamics Approach. (449 K)
Franaszek, M.; Simiu, E.

International Journal of Non-Linear Mechanics, Vol. 31, No. 6, 861-869, 1996.

Sponsor:

Office of Naval Research, Washington, DC

Keywords:

noise (sound); columns; chaotic dynamics approach equations; equations

Abstract:

For a spatially-extended dynamical system we illustrate the use of a chaotic dynamics approach to obtain criteria on the occurrence of noise-induced escapes from a preferred region of phase space. Our system is a buckled column with continuous mass, subjected to a transverse continuously distributed load that varies randomly with time. We obtain a stochastic counterpart of the Melnikov necessary condition for chaos - and snap-through - derived by Holmes and Mardsen for the harmonic loading case. Our approach yields a lower bound for the probability that snap-through cannot occur during a specified time interval. In particular, for excitation with finite-tailed marginal distribution, a simple criterion is obtained that guarantees the non-occurrence of snap-through.