Model-free nonlinear restoring force identification for SMA dampers with double Chebyshev polynomials: approach and validation

Abstract

The initiation and propagation of damage such as cracks in an engineering structure under dynamic loadings is a nonlinear process. Strictly speaking, conventional eigenvalue and eigenvector extraction-based damage identification approaches are suitable for linear systems only. Due to the unique nonlinearities associated with each civil engineering structure, it would be inefficient to attempt to express the nonlinear restoring force (NRF) of an engineering structure such as a reinforced concrete structure in a parametric form. Consequently, it is highly desirable to develop a general nonlinear identification approach to achieve structural damage detection in both qualitative and quantitative ways without the assumption on the parametric model of the hysteretic behavior. In this paper, based on a double Chebyshev polynomial function, a time-domain identification approach is proposed for identifying both the structural NRF and the mass distribution for multi-degree-of-freedom (MDOF) structures under incomplete dynamic loadings. As a typical nonlinear material, shape memory alloy (SMA) is introduced to a MDOF structural model to mimic the nonlinear behavior under dynamic loadings. The feasibility and robustness of the proposed approach is validated via (1) a numerical MDOF structure model equipped with a SMA damper whose restoring force is described by a double-flag-shaped nonlinear model, and (2) an experimental study on a four-story shear building structure model equipped with an in-house design of a SMA damper used to mimic the structural NRF under incomplete impact loadings. The identified NRF is compared with the theoretical values and the measurements in experiment. Both numerical and experimental results show that the proposed approach is capable of identifying both the mass distribution and structural nonlinearity under dynamic loadings, and could be potentially used for damage initiation and propagation monitoring during vibration of engineering structures under dynamic excitations.