Stochastically Excited Linear Nonconservative Systems

Dynamic stability of linear nonconservative systems under stochastic parametric excitation of small intensity is examined. It is assumed that a finite number of modes of a general. multi-degree-of-freedom system undergo flutter instability (nonresonance case). A modified stochastic averaging method is employed to obtain the contribution from the stochastic components of the stable modes to that of the critical modes. The approximate ItÔ equations tor the critical modes are then examined. Conditions for mean square stability of dynamic response are obtained. Results are shown to depend only on those values of the excitation spectral density near twice the natural frequencies, the difference and combination frequencies of the system. The results are applied to the problem of a cantilever column subjected to stochastic follower force.