Research On Theory And Method Of Quadratic Finite Element Model Updating

The model updating problem appeared in the early 1990 s as an important tool for construction and maintenance of mechanical system.The research on the quadratic model updating is an important international front problem nowadays.In recent years,the research on the quadratic model updating has obtained a lot of research results at home and abroad,but there are still many problems to be studied more in-depth,such as how to remain the coefficient matrix positive definite,physical connectivity under specific conditions.According to the real symmetric quadratic model,the new direct method and efficient optimization technology of the development model updating,so that quadratic model updating can not only remain the original quadratic model structure,but also satisfy no spillover,and still need more in-depth study.The quadratic finite element model updating problem concerned a secondary vibration system,using partial measurement characteristic pair to replace the characteristic pair that need to be replaced in the initial model,the original quadratic model is replaced by new quadratic model,so that remaining the feature is consistent with the original model.In practice,the observation data are usually incomplete,such as the partial column vector of measurement characteristic pair is complete,but the residual column vector is partially known,or each column vector are incomplete.This paper will study these problems.This paper studies the real quadratic model of partial incomplete measured data and no spill-over.This paper first(i)introduces two different methods of construction method and matrix method,then(ii)quadratic model updating with partial incomplete measurement is solved by the matrix block and Kronecker product,and the expression of solution and solvable conditions of the problem are given by studying the problem.The problem is mainly used to solve the measurement of partial data in the measurement spectral information,that is,when some data is difficult to measure,we can use this method to solve the problem,finally(iii)the expression of the solution of the quadratic model updating is expressed by the construction method in a special case.The main research results:(i)using matrix block method to solve measurement data is not easy to measure the spectral information,and the expression of solution and solvable conditions of the problem are given;(ii)when the half of the feature pairs are modified,the quadratic model updating problem is given by using the construction method,and the solution does not contain the parameters.In this paper,the theory and method of the quadratic finite element model updating will enrich the content of numerical algebra,provide a certain method and theoretical support for vibration subject.