Study On Model Updating And Identification Of Structural Localized Nonlinearities

Finite element model has been widely used in many engineering fields.However,due to parameter errors,order errors and structural manufacturing errors,the initial modeling often cannot accurately represent the real structure.Based on structural features obtained from experimental data,the model updating theory modifies the initial modeling to make it closer to the actual structure.After years of development,the model updating theory has become more and more mature and began to play a role in real engineering structures;Especially in the rapidly developing theoretical system of structural health monitoring in recent years,structural damage identification based on model updating has become an important theoretical research content.However,the traditional model updating theory requires studied structures to be linear,so it cannot deal with structures with nonlinear elements.At present,modern structures’nonlinear behavior cannot be ignored more and more.If it is not properly considered in the process of modeling and experiment,it is difficult to ensure structural safety.For example,the overall collapse of Tacoma Canyon Bridge in the United States is due to the failure to consider the intrinsic nonlinear characteristics.Therefore,it is urgent to develop the nonlinear model updating theory.Nonlinear model updating pushes the envelope of the traditional model updating theory.In this thesis,for the structures with localized nonlinearities,nonlinear system identification theory and traditional model updating theory are integrated,and a nonlinear model updating strategy is proposed,which includes nonlinearity detection,nonlinearity characterization,nonlinear structures’ underlying linear model updating and nonlinear model updating objective function;This thesis studies these four aspects as follows:In terms of nonlinearity detection,firstly,the calculation method of complex analyzed Hilbert transform is deduced by using residue theory.Then combined with the nonlinearity detection method based on Hilbert transform,the nonlinearity detection criterion based on complex analyzed Hilbert transform is proposed,which avoids the truncation error of Hilbert transform calculated by numerical integration and its false alarm for nonlinearity detection.Numerical examples and experimental studies verify the effectiveness and accuracy of the theoretical derivation and the proposed nonlinearity detection criterion.In the aspect of nonlinearity characterization,based on the nonlinear modal analysis theory,the checking criterion of structural steady-state response for steady-state sinusoidal sweep test is proposed,which improves the reliability of obtaining the amplitude-frequency characteristic results of nonlinear structures and alleviates the defect of lengthy testing time under sinusoidal excitation type.At the same time,a backbone curve extraction method of nonlinear systems based on the first-order harmonics under free-vibration time-history response signal is proposed,which avoids the additional interpolation calculation and signal preprocessing process of traditional methods;Numerical examples and experimental studies verify the effectiveness and accuracy of the steady-state response checking criterion and the backbone curve extraction method,and illustrate the role of backbone curve in the process of nonlinearity characterization.Based on the partial coherence theory,the linear frequency response function is separated from the frequency response function directly extracted from the tested nonlinear structure,and the underlying linear model updating strategy based on the frequency response function is proposed;Moreover,the model updating method based on frequency response function in this strategy combines Sherman-Morrison-Woodbury formula and frequency response function similarity metric,which is also a new linear model updating method based on frequency response function;Numerical examples and experimental studies verify the effectiveness and accuracy of the method in linear and underlying linear model updating and damage identification.Model updating is a comprehensive process of experiment and modeling,and the two aspects are finally connected by the updating objective function.In terms of nonlinear model updating objective function in the proposed nonlinear model updating strategy,firstly,using the relative coordinate expression of nonlinear structures,a local equivalent linearization numerical calculation method is proposed to extract the equivalent linear system from the test data directly.On this basis,the nonlinear model updating objective function based on the local equivalent linear system is established.Numerical examples are given to verify the effectiveness of the local equivalent linearization method and its nonlinear model updating objective function,and to verify the effect of this method on improving accuracy of nonlinear models.