The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom
linear systems subjected to white noise parametric excitation are investigated.
Through a perturbation method we obtain the explicit asymptotic expressions
for these exponents in the presence of low intensity noise. The Lyapunov
exponent and moment Lyapunov exponents are important characteristics for
determining the almost-sure and moment stability of a stochastic dynamical
system. As an example, we study the almost-sure and moment stability of the
flexural-torsion stability of a thin elastic beam subjected to a stochastically
fluctuating follower force. The validity of the approximate results for moment
Lyapunov exponents is checked by a numerical Monte Carlo simulation for these
stochastic systems.
Keywords
elastic beam, eigenvalue, perturbation, stochastic
stability, mechanics of solids and structures