Stochastic Modal Appropriation Method: Time Domain Extension for MDOF Systems

In this paper, the operational modal analysis (OMA) method called Stochastic Modal Appropriation (SMA) has been extended to deal with Multi Degree of Freedom (MDOF) dynamic systems. The SMA algorithm, originally developed in the time domain to identify a Single Degree of Freedom (SDOF) uncoupled modal system, allows one to estimate natural frequencies and damping ratios, with no information about the mode shapes. Here, the SMA method has been extended to estimate mode shapes. This unique mode shape estimation is carried out by applying the appropriation condition simultaneously to the set of the correlation functions evaluated, in turn, from the system output responses only. The theoretical derivation of the proposed method is briefly presented and numerical validations are performed to characterize the accuracy of the modal parameter estimates. Such numerical analyses are carried out by using Matlab and MSC.NASTRAN commercial codes. Then, the developed algorithm is tested on real responses of structures through experimental analysis. Two structures are taken into account: a cantilever beam and a cantilever plate.