科研之友
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摘要
Finite element model updating is a procedure to minimize the differences between analytical and experimental results and can be mathematically reduced to solving the following problem. Problem P: Let M-a is an element of SRnxn and K-a is an element of SRnxn be the analytical mass and stiffness matrices and Lambda = diag{lambda(1),...,lambda(p)} is an element of R-pxp and X = [x(1),...,x(p)] is an element of R-nxp be the measured eigenvalue and eigenvector matrices, respectively. Find ((M) over cap, (K) over cap) is an element of S-MK such that parallel to(M) over cap - M-a parallel to(2) + parallel to(K) over cap - K-a parallel to(2) = min((M,K)is an element of SMK) (parallel to M - M-a parallel to(2) + parallel to K - K-a parallel to(2)), where S-MK = {(M, K)vertical bar X-T MX = I-p, MXA = KX} and parallel to.parallel to is the Frobenius norm. This paper presents an iterative method to solve Problem P. By the method, the optimal approximation solution ((M) over cap, (K) over cap) of Problem P can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrix pair. A numerical example shows that the introduced iterative algorithm is quite efficient.
