New model updating method for damped structural systems

作者：Liu Hao^*; Yuan Yongxin

来源：Computers & Mathematics with Applications, 2009, 57(5): 685-690.

DOI：10.1016/j.camwa.2008.10.069

• Inverse problem
• Damped structural systems
• Quadratic eigenvalue problem
• Model updating
• Best approximation

In this paper, the following two problems are considered:
Problem I Given a full column rank matrix X is an element of R(nxk), a diagonal matrix Lambda is an element of R(kxk)(k <= n) and matrices M(a) is an element of R(nxn), C(0), K(0) is an element of R(rxr), find n x n matrices C, K such that M(a)X Lambda(2) CX Lambda KX = 0, s. t. C([1, r]) = C(0), K([1, r]) = K(0), where C([1, r]) and K([1, r]) are, respectively, the r x r leading principal submatrices of C and K.
Problem II Given n x n matrices C(a), K(a) with C(a)([1, r]) = C(0), K(a)([1, r]) = K(0), find ((C) over cap, (K) over cap) is an element of S(E), such that vertical bar vertical bar C(a) - (C) over cap vertical bar vertical bar(2) vertical bar vertical bar K(a) - (K) over cap vertical bar vertical bar(2) = inf((C,M)is an element of SE) (vertical bar vertical bar C(a) - C vertical bar vertical bar(2) vertical bar vertical bar K(a) - K vertical bar vertical bar(2)), where S(E) is the solution set of Problem I.
By applying the theory and methods of the algebraic inverse eigenvalue problems, the solvability condition and the general solution to Problem I are derived. The expression of the solution to Problem II is presented.

• 出版日期2009-3
• 单位江苏科技大学; 南京航空航天大学