A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh. / Ph. D.