This study examines the vibration of rotating beams with double tapered geometry utilizing BFGMs. Material properties of the beams are power law distributed in the x and z directions. The stiffness and mass matrices are derived employing the Reddy formulation, also known as the Third-order Shear Deformation Theory (TSDT). Our main goal is to analyze the impact of material distribution, taper ratios, and rotational speed on beam natural frequencies. The obtained results are compared to previous research, demonstrating strong agreement and confirming the reliability and effectiveness of our approach. The study revealed that increasing the taper ratio in the width direction led to a higher natural frequency. Conversely, increasing it in both the height and width directions or in the height direction alone resulted in a lower natural frequency, except for the first mode.