SMA nonlinear restoring force identification for MDOF structures under dynamic loadings with double chebyshev polynomial
XU Bin1,2，XIN Lu-lu1，HE Jia3
1.College of Civil Engineering, Hunan University, Changsha410082，China；2.MOE Key Lab of Building Safety and Energy Efficiency (Hunan University), Changsha 410082，China；3.Department of Civil and Structural Engineering, Hongkong Polytechnic University, Hongkong 999077，China
Abstract：The initiation and development of damage 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. Due to the uniqueness of nonlinearity of different engineering structures, it is difficult to express the restoring force in a parametric form and it is highly desired to develop a general structural nonlinearity identification approach for structural damage detection in both qualitative and quantitative ways. In this paper, a double chebyshev polynamial model is employed to model the nonlinear restoring force and a time domain nonlinear shape memory alloy (SMA) restoring force identification approach was proposed for MDOF structures under dynamic loadings when the mass distribution of the structure is unknown and the structure is completely and incompletely excited. The feasibility and robustness of the proposed approaches were illustrated via numerical simulation with a MDOF structure equipped with a SMA damper with double flag-shaped nonlinear model considering the effect of noise and dynamic test measurements with a 4-story steel frame equipped with a SMA damper to mimic structural nonlinear performance. Numerical results are compared with that of the previously proposed power polynominal based approach. Results show that the proposed approaches are capable of identifying the nonlinearity and the mass distribution of the structure and are applicable for damage initiation and propagation process monitoring and quantitative evaluation of energy consuming during vibration of engineering structures under dynamic excitations.
2014, Vol. 33 
