Vibration characteristics of a tapered- pre-twisted-rotating blade made of Ti-6Al-4 V and ZrO₂ type of functionally graded material

A structural dynamic model is crucial due to the frequent variation in properties of the material along the direction of thickness of blade, necessitating computationally expensive finite element modeling with numerous layers for accurate representation. This study explores the free vibration characteristics of a rotating, pre-twisted, tapered blade made of ‘Functionally Graded Material (FGM)’using a structural dynamic model. It examines parameters such as rotating speed, Pre-twist angle,Hub radius, volume fraction index, and taper ratios for their impact on the Vibration Characteristics of the blade. The mathematical modeling of the blade employs the assumed mode method discovered by Rayleigh and Ritz, with motion equations developed using Lagrange’s equation. The study outlines a procedure for obtaining the stiffness and mass matrices of pre-twisted-tapered rotating blades, treating them as Euler–Bernoulli beams. Validation against existing methods illustrates the computational efficiency of the proposed method. The analysis focuses on functionally graded materials, particularly a Ti-4Al-6 V and ZrO₂ composite, widely used in the automobile and aerospace industries. It reveals that increasing the volume percentage of Ti-6Al-4 V enhances stiffness and natural frequencies. ZrO₂-rich FGMs exhibit a decrease in the first natural frequency with increasing pre-twist angle, while increasing blade speed decreases both natural frequencies. Moreover, increasing width and thickness taper ratios significantly increases both natural frequencies. Ultimately, increasing the volume percentage of Ti-6Al-4 V and setting high taper ratios can enhance the values of natural frequencies of pre-twisted tapered blades made of Ti-6Al-4 V and ZrO₂ FGMs, benefiting applications requiring high strength-to-weight ratios.