New model updating method for damped structural systems

  • Authors:

  • Hao Liu;Yongxin Yuan

  • Affiliations:

  • Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China;Department of Mathematics, Jiangsu University of Science and Technology, Zhenjiang 212003, PR China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

In this paper, the following two problems are considered: Problem I Given a full column rank matrix X@?R^n^x^k, a diagonal matrix @L@?R^k^x^k(k@?n) and matrices M"a@?R^n^x^n,C"0,K"0@?R^r^x^r, find nxn matrices C,K such that M"aX@L^2+CX@L+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 rxr leading principal submatrices of C and K. Problem II Given nxn matrices C"a,K"a with C"a([1,r])=C"0,K"a([1,r])=K"0, find (C@?,K@?)@?S"E, such that @?C"a-C@?@?^2+@?K"a-K@?@?^2=inf"("C","M")"@?"S"""E(@?C"a-C@?^2+@?K"a-K@?^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.