In-Situ Component-Based TPA for Time-Variant Dynamic Systems: A State-Space Formulation

In this chapter, a methodology to calculate equivalent forces by taking into account the possible time-varying dynamic behavior of the components under analysis is presented. This methodology is based on the use of the state-space realization of the in-situ component-based TPA method. To take into account possible time-varying dynamic behavior of the systems under study, a local linear parameter varying (LPV) model identification approach is used. This approach enables the computation of state-space models representative of the components at each time instant by interpolating a given set of linear time-invariant (LTI) state-space models representative of the dynamics of the components under study for fixed operating conditions. By exploiting a numerical example, it is found that when dealing with structures presenting time-varying behavior, accurate equivalent forces can be computed in time domain by using the approaches presented in this chapter. Furthermore, it is clearly demonstrated that ignoring the time dependency of the dynamic behavior of mechanical systems can lead to an important deterioration of the results.