TABLE OF CONTENTS Some topics related to vibration reanalysis are introduced in this chapter. Calculation of the first-mode shape by the matrix iteration approach is demonstrated in Section 12.1, and formulation of eigenproblem reanalysis is presented in Section 12.2. A distinction is made between the following two types of reanalysis problems:
Eigenvector reanalysis, where the object is to calculate the modified eigenvectors, or mode shapes, due to changes in the stiffness matrix and in the mass matrix. This type of problem, which is more difficult to solve than the eigenvalue reanalysis problem, can be solved by the CA method [1] , [2] as is shown in Section 12.3.
Eigenvalue reanalysis, where the object is to calculate the modified eigenvalues due to changes in the stiffness and mass matrices. In many optimal design problems we are interested only in the eigenvalues rather than the eigenvectors. It is often assumed that the mode shapes change only insignificantly due to changes in the design. The eigenvalue reanalysis problem, which can be solved by several methods, is discussed in Section 12.4.
[1]Kirsch, U. Combined approximations - a general reanalysis approach for structural optimization, Structural Optimization 20 (2000) 97 106.
[2]Aktas, A. and Moses, F. Reduced basis eigenvalue solutions for damaged structures, Mechanics of Structures and Machines 26 (1998) 63 79.
Consider the generalized eigenproblem presented in Section 2.4.1 [Eq. (2.55)]
where ? is the circular frequency, ? 2 = ? are the eigenvalues indicating the square of...
