A new stochastic analysis for multiple supported MDOF secondary systems: I. Dynamic interaction effects

A new stochastic analysis is developed to estimate the response of multiply-supported multi-degree-of-freedom (MDOF) secondary systems to dynamic loading. In the proposed stochastic analysis, the effect of the dynamic interaction between the secondary and primary systems is included. An outline for the theoretical formulation of the proposed stochastic analysis is presented. The dynamic interaction is shown to consist of two effects: the effect of the interaction forces developed at the attachment points, and the effect of the changes in the primary system properties as a result of the attachment of the secondary system. Numerical examples are provided to demonstrate the proposed analysis.