A matrix iterative method is developed for modal sensitivity analysis of structures, which can be utilized to both distinct and repeated eigenvalue cases. The novel method needs only firs: order derivatives of the system matrices in the repeated eigenvalue case, and is easy to be implemented. A matrix iterative algorithm is presented based on the existence and uniqueness of the governing equations for eigenvector sensitivities computation with multiple eigenvalues. Pre- and post-error-estimation formulas are 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 analysis method.
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