Localization,Model And Parameter Identification Of Local Nonlinearity In Structural Systems

It is well known that lots of structures in engineering contain various kinds of nonlinear factors.Studies on identification techniques for these nonlinear structures provide reliable guidance for their dynamical property analysis and optimization design.In many situations,nonlinearities in these structural systems usually appear at the positions of the connection and boundary in structures,which gives nonlinearities the strong local characteristic.Therefore,with the assumption that the positions of nonlinearities are sparse and the types of nonlinearities are arbitrary,researchers put forward the concept of locally nonlinear system which can be decoupled into underlying linear system and locally nonlinear part.Relevant theories and methods on identification of the locally nonlinear system are developed to achieve mathematical models with clear and definite physical meanings.This dissertation focuses on theories and methods of three parts of the identification problem for the locally nonlinear system:localization,model identification and parameter identification.The main research contents are summarized as follows:(1)Studies on nonlinearity localization based on subsystem's linear factor.The dissertation puts forward the linear factor criterion using stochastic subspace theory to detect subsytems'nonlinearities in the multi-degree of freedom lumped mass system.Based on the linear factor,a nonlinearity localization method is proprosed and then verified by numerical simulations.The analysis of method's performance under different levels of noises,different strengths and types of local nonlinearities is given.Results show that the method has good performance and noise robustness when localizing these different kinds of nonlinearities.(2)Studies on local nonlinearities'model identification based on the integrity index.Based on the reverse path method,the integrity index which measures the rationality of the nonlinear basis functions is proposed.Further more,a forward selection algorithm which can achieve local nonlinearity's descriptive form efficiently and is thus especially suitable for the large nonlinear basis function set is proposed.The algorithm is verified by numerical simulations of a six degrees of freedom system and a cantilever structural system.(3)Studies on local nonlinearities'parameter identification based on the stochastic subspace theory.The dissertation studies three contents in nonlinear subspace method:generalized frequency response function,algorithm to estimate state space equation and similarity matrix irrelevance.The dissertation also studies effects of sample frequency to the performance of the traditional nonlinear suspace method under different levels of noises,and proposes the dual-frequency nonlinear subspace method,which reduces the effect of the sample frequency.Besides,based on effects of system's order to the identification result,the dissertation proposes a two-step nonlinear subspace method.The method needs measurements under two different levels of excitations and is able to determine a more suitable order and give out more accurate identification results than the traditional nonlinear subspace method.(4)Experimental studies on the locally nonlinear structural system.The experimental structure is a beam with a flexible thin steel sheet.Nonliearity in the system is the cubic stiffness nonlinearity which comes from the large deformation geometric nonlinearity caused by the thin steel sheet.In the experimental study,the local nonlinearity is detected by the frequency response function and coherence function,the form of the nonlinearity is determined by the integrity index,and then the two-step nonlinear subspace method is used to identify the frequency response function of the underlying linear system and the coefficient of the locally nonlinear basis function.The identification result is verified by the H_v estimation of frequency response function under the low level of excitation.