Random Vibration of Systems with Frequency-Dependent Parameters or Fractional Derivatives

Abstract

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 representations of dynamic systems or convolution integrals; the motion of these systems is governed by integrodifferential equations, and related Monte Carlo simulations can be conducted expeditiously. It is shown with mathematical rigor that the response of these systems to random excitation can be determined by a standard formula.