Aeronautical structures, such as aircraft or missiles, are usually highly sophisticated systems often subjected to random vibration environment. Thus, in various design, development, and production stages, laboratory random vibration testing of sampled solid rocket motors on electromagnetic or hydraulic shakers are routinely performed as an important experiment-oriented quality control strategy. Nevertheless, it is crucial to understand the dynamic structural behavior of these layered viscoelastic cylinders such as solid rocket motors under random vibration tests analytically. In this study, a methodology has been developed to deal with the random vibration of a general class of composite structures with frequency-dependent viscoelastic material properties as represented by the example of solid rocket motors. The method combines the finite element method, structural dynamics, strain energy approach, and random vibration analysis concepts. The method is a more powerful technique capable of treating sophisticated random vibration problems with complicated geometry, nonhomogeneous materials, and frequency-dependent stiffness and damping properties. Before the random vibration analysis could proceed, a microcomputer-based dynamic mechanical analyzer system was used together with time-temperature superposition principle to obtain the frequency-dependent dynamic viscoelastic properties of the solid propellant. The strain energy approach has been used to calculate the frequency-dependent equivalent viscoelastic damping which is in turn judiciously represented by a combination of viscous damping and structural damping to accommodate this frequency dependent material property. Modal analysis data together with half power band width calculated at each natural frequency are highly useful guides in the harmonic analysis to achieve computational efficiency. On one hand, the technique used in this study has a hybrid taste in the sense that it makes use of best features and capabilities of both modal analysis and harmonic analysis to achieve the goal of random vibration analysis in addition to the power of finite element technique. The displacement, acceleration and stress power spectra have been obtained for significant points on the rocket model together with their root mean square values. These data can be used for various analyses, testing, design, and other purposes as discussed in later sections of this study. / Ph. D.