Dominant parameters of uncertain complex dynamic systems

The relationships between the parameters of a structural system and its wide-band response is explored. The central goal of this paper is to identify and characterize critical system configurations for which the response may become highly sensitive to small parameter variations. The examination of analytical expressions for mode derivatives and mean-square response of certain fundamental systems has shown that critical systems can be defined by a mode crossing set in the space of variable parameters. The relationships between the mode crossing set and the system response, and the impact on analysis of systems with uncertain parameters are explored. It is concluded that the wide-band response of structural systems have complex characteristics which must be considered for accurate and meaningful analysis of uncertainties or parameter variations.