Noise-Induced Snap-Through of a Buckled Column With Continuously Distributed Mass: A Chaotic Dynamics Approach.
Noise-Induced Snap-Through of a Buckled Column With
Continuously Distributed Mass: A Chaotic Dynamics
Franaszek, M.; Simiu, E.
International Journal of Non-Linear Mechanics, Vol. 31,
No. 6, 861-869, 1996.
Sponsor:Office of Naval Research, Washington, DC
noise (sound); columns; chaotic dynamics approach
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.