Flapwise bending vibration of rotating tapered Rayleigh cantilever beams

• Flapwise bending vibration of rotating tapered cantilever beams is studied.
• Vibration of non-uniform beams with power-law varying width and height is analyzed.
• Effects of rotary inertia and angular velocity on the natural frequencies are discussed.
• The taper ratio and hub radius have a strong influence on the natural frequencies.
• Resonance takes place for certain rotating velocity.

Free vibration of rotating tapered cantilever beams with rotary inertia is studied.The cross-sectional area and its moment of inertia vary along the length. The governing differential equation of vibration of rotating Rayleigh beams is derived using Hamilton's principle, and the integral equation method is proposed to determine the natural frequencies. For rotating non-uniform beams with power-law varying width and height, numerical results of the natural frequencies are obtained for different taper ratios, angular velocities and hub radii. The solutions are validated by comparison with the results in open literature. The effects of the rotary inertia, angular velocity, taper ratio and hub radius are analyzed and presented in tables and graphs. Resonance is also analyzed.