Sensitivity derivatives of eigendata of one-dimensional structural systems

A general formulation based on the transfer matrix is presented to calculate the sensitivity derivatives of eigenvalue problems of one-dimensional structural systems. The method is equally applicable to any discrete or distributed system of one variable. The formulation is applied to determine the sensitivity derivatives of eigendata of a rotating helicopter blade and also to an optimization problem of a cantilever beam with frequency constraints. It is found that the computational efficiency of the present method is superior to those of the existing methods by an order of magnitude and that this efficacy improves with increasing numbers of design parameters and degrees of freedom.