RANDOM VIBRATION OF SYSTEMS WITH FREQUENCY-DEPENDENT PARAMETERS OR FRACTIONAL DERIVATIVES

This technical note considers a class of models that describe dynamic systems with frequency-dependent parameters or fractional derivatives. These concepts are elucidated by introducing abstract state-space rep resentations of dynamic systems or convolution integrals; the motion o f these systems is governed by integrodifferential equations, and rela ted Monte Carlo simulations can be conducted expeditiously. It is show n with mathematical rigor that the response of these systems to random excitation can be determined by a standard formula.