Nonlinear Structural Identification Based On Volterra Series

Nonlinearities in engineering structures can generally be classified into geometric nonlinearity,physical nonlinearity and boundary nonlinearity.Geometric nonlinearity refers to the nonlinear problem caused by the large deformation of the structure.And the geometric equation no longer maintains the linear relationship.The physical nonlinearity is caused by the stress-strain relationship or the constitutive equation of the material is not linear.The boundary nonlinearity refers to the nonlinear problem caused by the boundary constraint of the structure not satisfying the linear relationship.There are always various nonlinear problems in the engineering structure due to the material's own performance defects,improper manual operation and various natural factors.Such as the large gantry structure has gaps and frictions due to looseness or breakage of the connecting bars and so on.And the structural nonlinearity is usually accompanied by structural damage or failure.If it is not monitored and allowed to develop,it will cause immeasurable harm to the quality of the engineering structure.Therefore,it is necessary to timely monitor the structure health,accurately identify early nonlinearities,and take corresponding repair measures to reduce property losses and casualties.The first chapter of this paper discusses the background and significance of nonlinear structural identification.And then summarizes the research status of nonlinear structural identification.Finally summarizes the main research contents of this paper.The third chapter studies the nonlinear detection of structures based on the time domain representation of Volterra series.And based on the homogeneous solution of Volterra series,the contribution of each order of the series to the response is obtained.Then bring it into the third-order autocorrelation function method.The structural nonlinearity is judged by the result of the third-order autocorrelation function being zero or non-zero.To verify the effectiveness of the method,the above method is applied to the Duffing nonlinear system and Van der Pol nonlinear system.Numerical results show that the third-order autocorrelation function results are not zero for the above two nonlinear systems whether using the first two orders of the system or the first three orders of response to approximate the actual response of the system.It is shown that the third-order autocorrelation function method can effectively detect nonlinearity.The fourth chapter introduces the method theory of general least squares and recursive least squares.Then applies the recursive least squares method to solve the Volterra time domain kernels.Furthermore,nonlinear index VH are proposed.VH₂ is the average of the absolute values of the second-order time-domain kernels andVH₃ is the average of the absolute values of the thirs-order time-domain kernels.Nonlinear detection and description of the degree of nonlinearity are achieved by comparing changes in nonlinear index under different conditions.In order to verify the proposed nonlinear index for structural nonlinear identification,the above solution method is applied to the Duffing nonlinear system and a 4degree-of-freedom structure at Los Alamos Naional Laboratory?LANL?.The numerical simulation results show that the proposed nonlinear index can effectively determine the nonlinear state of the system.And the nonlinear index VH is positively correlated with the degree of nonlinearity of the system.In the fifth chapter,the nonlinear localization of multi-degree-of-freedom systems is studied based on the frequency domain representation of Volterra series,and the nonlinear positioning criterion is proposed.And proposes a NOFRF solving method based on recursive least squares algorithm.Compared with general least squares,the newly proposed method can obtain the different order NOFRF of each mass of the system according to the excitation signal and response signal of the system with only one excitation.The solution process does not involve matrix inversion and the solution is more efficient.Finally gives a numerical example of a 4 degree-of-freedom nonlinear structure.Under different conditions,numerical results show that bringing the solved NOFRF into the nonlinear positioning theory can correctly and efficiently determine the location of the nonlinear.This verifies the accuracy of the NOFRF method and the validity of the nonlinear localization theory.Finally the research of this paper is summarized.And the research on nonlinear identification of structures using Volterra series is discussed and prospected.