Alpha-cut robust design of a fractional-order fuzzy tuned mass damper for targeted-band vibration suppression in rotating machinery

Abstract

This study presents a targeted-band design method for suppressing flexible-rotor vibration using a fractional-order fuzzy tuned mass damper. A force-excited rotor-support mode represents the host machine, while the absorber branch comprises a spring and fractional dashpot. The absorber parameters are selected to minimize the primary displacement peak while remaining robust to bounded uncertainty in mass ratio, tuning ratio, damping index, fractional order, support stiffness, and force level. Triangular fuzzy numbers are propagated through alpha-cut intervals, and the resulting frequency-response envelopes are optimized by a weighted objective that penalizes high peaks and wide uncertainty spreads. Closed-form frequency-response relations evaluated directly at interval corners keep the procedure transparent and reproducible. For a rotor-support oscillator with natural frequency 9.762 Hz, primary mass 42 kg, primary stiffness 158,000 N/m, force amplitude 58 N, and mass ratio μ = 0.05, the optimized design yields a central peak displacement of 1.929 mm and an alpha-zero upper peak of 3.154 mm, compared with 10.197 mm for the uncontrolled system and 2.028 mm for the deterministic Den Hartog reference. Evaluation at μ = 0.03, 0.05, and 0.07 shows consistent peak reduction and useful trends for initial parameter tuning. The method therefore provides bounded vibration envelopes, tuning guidance, stroke estimates, and sensitivity rankings for uncertain rotating-machine data within the specified target band.