state transition matrix

This paper discusses an adaptation of modal analysis concepts to time-varying periodic systems. It will be shown that the pseudo-modal parameters preserve certain properties of the conventional modal parameters defined for LTI systems. For this reason، after definition of pseudo modal parameters for time varying systems، a new modal analysis method will be introduced in time domain and it will be shown that these parameters could explain the nature of system. For periodic time varying systems، state transition matrices are formed by an ensemble set of responses which are obtained through multiple experiments on the system with the same time varying behavior. In next step the pseudo natural frequencies of a beam with moving mass using introduced method will be extracted. In final، it will be proved that for a linear time periodic system، the pseudo natural frequency treats periodic too.