Short-term flutter-type instability of undamped tdof system with randomly varying bifurcation parameter

A model problem of a two-degrees-of-freedom (tdof) flutter is considered for an undamped system with random temporal variations of its bifurcation parameter. The nominal system, i.e. one with the mean value of the bifurcation parameter is assumed to be stable; however the above variations may occasionally bring the system temporarily into its domain of dynamic instability. A procedure for predicting probability density function (PDF) of the peaks of the corresponding intermittent response is outlined as based on parabolic approximation for the parameter variation in the vicinity of its peaks. For the case of relatively slow parameter variations the equations of motion are reduced by Krylov–Bogoliubov averaging to those describing static instability of the response amplitude. The basic relation between peak values of the bifurcation parameter and of the corresponding response outbreak for the reduced system is therefore available from previous studies of short-term static instability in a sdof system.