Abstract
A combined method for calculating particular solutions of eigenvector derivative governing equations in the generalized eigenproblem with groups of repeated eigenvalues is presented, which finds the first set of the particular solutions by a direct method and the other particular solutions by a family of modal methods. The direct method is based on Gauss elimination, by which the constraint generalized inverse of the frequency shift stiffness matrix can be obtained, as well as the particular solution, and the method is applicable to all nondefective systems. A formula for finding a constraint generalized inverse from another is derived by which the total calculation can be reduced. A simple calculating example is included.
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