M. Franaszek et E. Simiu, NOISE-INDUCED SNAP-THROUGH OF A BUCKLED COLUMN WITH CONTINUOUSLY DISTRIBUTED MASS - A CHAOTIC DYNAMICS APPROACH, International journal of non-linear mechanics, 31(6), 1996, pp. 861-869
For a spatially-extended dynamical system we illustrate the use of a c
haotic 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 cont
inuously distributed load that varies randomly with time. We obtain a
stochastic counterpart of the Melnikov necessary condition for chaos-a
nd 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 excitations with finite-tailed marginal distribution, a simple cr
iterion is obtained that guarantees the non-occurrence of snap-through
. Copyright (C) 1996 Published by Elsevier Science Ltd.