In this study, the free vibration analysis of rotating and non-rotating fiber metal laminate (FML) beams, hybrid composite beams (HCB), and functionally graded beams (FGB) are investigated. FML beams are high-performance hybrid structures based on alternating stacked arrangements of fiber-reinforced plastic (FRP) plies and metal alloy layers. Hybrid composite beams are materials that are made by adding two different fibers. Functionally graded beams are new materials that are designed to achieve a functional performance with gradually variable properties in one or more directions. The effects of different metal alloys, composite fibers, and different aspect ratios and angular velocities on the free vibration analysis of FML beams are studied. The effects of different angular velocities and different aspect ratios of rotating and non-rotating hybrid composite beams are also investigated. Finally, the effects of different angular velocities and different material distributions, namely the power law, exponential distribution, and Mori Tanaka's scheme on the free vibration analysis of FGB, are also invesigated.