Identification of SMA dampers nonlinear restoring force of incompletely excited MDOF structures with double polynomial model

The initiation and development of damage such as cracks in an engineering structure under dynamic loadings is a typical nonlinear process. Strictly speaking, the conventional vibration and eigenvalues extraction based damage identification approaches are suitable for linear systems only. In this paper, based on a double Chebyshev polynomial model, a time-domain NRF identification approach is proposed for identifying the structural nonlinearity as well as the mass distribution under incomplete dynamic loadings. The feasibility and robustness of the proposed approach is validated via a numerical MDOF structure equipped with a shape memory alloy (SMA) damper whose restoring force is modeled by a double-flag-shaped nonlinear model. Results show that the proposed approach is capable of identifying the mass distribution and structural nonlinearity, and could be potentially used for monitoring damage initiation and propagation processes during vibration of engineering structures under dynamic excitations.