Nonlinear Restoring Force Identification Of MDOF Structures Under Dynamic Loadings

Damage identification and performance evaluation of engineering structuresunder strong dynamic loadings such as earthquake are the crucial problems need todeal with in the post-disaster relief, safety assessment and the restoration andreconstruction. The initiation and development of damage in an engineering structureunder dynamic loadings is a typical nonlinear process. Strictly speaking, theconventional vibration and eigenvalues extraction based identification approaches aresuitable for linear systems only. Due to the uniqueness of nonlinearity of differentengineering structures, it is highly desired to develop a general structural nonlinearityidentification approach for structural damage detection qualitatively andquantitatively.Based on the above background, the nonlinear restoring force was used as andirectly indicator to describe the structural nonlinear behavior, a general structuralnonlinearity identification approach was proposed and developed, providing a newway for the monitoring of the initiation and development of damage and thequantitative evaluation of energy assumption of engineering structures under dynamicexcitations. The main contents of this thesis include:1. For theoretical method, a nonlinearity identification approach for MDOFsystems based on double Chebyshev polynomial modal which can identify effectivelythe structural nonlinearity when the mass distribution is unknown was proposed.Based on information of the excitation and its dynamic response, through Least-squaremethod and Newton’s third law and from the structural dynamic equilibrium equation,two specific implementation processes under complete excitation and incompleteexcitation were discussed respectively.2. In the numerical simulation, three nonlinear members were used to mimicstructural nonlinearity and two cases which considering separately without noise andenvironmental noise impact were used to validated the effectiveness of the mentionedidentification method. Numerical results were compared with that of the previouslyproposed power polynominal based approach.3. In the experimental measurements, the feasibility of the nonlinearityidentification approach for MDOF systems based on double Chebyshev polynomialmodal was illustrated via a four-story steel frame structure which installed two MR dampers and a SMA damper which were employed to simulate structural nonlinearityand the comparative analysis between the recognition results and the measured data ofthe nonlinear restoring force of the MR dampers and the SMA damper.