A Matrix Iterative Method for Modal Sensitivity Analysis

A matrix iterative method is developed for modal sensitivify analysis of structures, which can be utilized ,a both distinct and repeated eigenvalue cases. The novel method needs only firs: order derivatives of the system motrices in the repeated e;genvalue case, and is easy to be implemented. A matrix iterative algorithm is presented based on the existence and uniqueness of the governing equations for eigmvector sensitivities computation with multiple e;genvalues. Preand post-error-estimation formulas m-e derived based on the convergence of the iteration algorithm. Computer simulations using a symmetrical cantilever beam and a 3-D FRAME structure with distinct, repeated and closed eigenvalues are conducted to show the effectiveness and accuracy of the proposed new modal sensitivity analysir method. NOMENCLATURE M,K : mass and stiffness matrices h : eigenvalue VA : eigenvectorlmode shape Y’,@ : eigenvector (mode shape) matrix N : number of DOFs in the FE model 1 : number of multiplicity of eigenvalues i,k : integer E : small positive number