New Methods for Finite Element Model Updating Problems

Abstract

We consider two finite element model updating problems, which incorporate the measured modal data into the analytical finite element model, producing an adjusted model on the (mass) damping and stiffness, that closely matches the experimental modal data. We develop two efficient numerical algorithms for solving these problems.The new algorithms are direct methods that require O O(nk 2 ) and O O(nk 2 + k 6 ) flops, respectively, and employ sparse matrix techniques when the analytic model is sparse. Here n is the dimension of the coefficient matrices defining the analytical model, and k is the number of measured eigenpairs. Nomenclature= adjusted stiffness matrix, n × n K a = stiffness matrix of the original FEM model, n × n k = number of measured eigenvalues or eigenvectors M = adjusted mass matrix, n × n M a = mass matrix of the original FEM model, n × n Q = orthogonal matrix, n × n R = upper triangular matrix, k × k= trace operator vec(·) = vectorization operator x = solution of linear system, k × 1 j = see Eq. (18); k × k δ = see Eq. (41) = diagonal block eigenvalue matrix, k × k λ = eigenvalues of quadratic eigenvalue problem μ = weight factor ν = weight factor = eigenvector matrix, n × k

A New Direct Method for Updating Mass and Stiffness Matrices with No Spillover

“…The effects of the modifications were determined from the corrected mass and stiffness matrices. Additionally, Kuo et al recently proposed a direct method which seemed more efficient and reliable [9]. The iterative updating methods use the sensitivity of the parameters to update the model.…”

Analytical dynamic model modification using acceleration and displacement feedback

“…Over the past 40 years, various techniques for updating mass and stiffness matrices for undamped systems using measured response data have been discussed by Baruch [2] , Baruch and Bar-Itzhack [3] , Berman [4] , Berman and Nagy [5] , Wei [6][7][8] , Yang et al [9] , Yang and Chen [10] , Yuan [11,12] and Yuan and Liu [13] . For damped structured systems, the theory and computation have been considered by Friswell et al [14] , Pilkey [15] , Kuo et al [16] , Chu et al [17] , Yuan and Dai [18] and Yuan and Liu [19] . Finite element model correction using a symmetric eigenstructure assignment was proposed in [20] and [21] .…”

Mass and Stiffness Updating Based on Normal Response Function Method

“…According to the literature review, model updating methods can be broadly classified into three major groups: direct matrix methods [1][2][3][4], parametric updating methods [5][6][7][8] and cross-model cross-mode (CMCM) method [9][10][11]. Direct matrix methods are generally of non-iterative methods, which is to modify the mass and stiffness matrices directly.…”