Rotating machinery support design with the aim of reducing the synchronous unbalance response has significant importance regarding the various applications of these machineries. In this paper, we present H∞ and H2 methods for calculating the optimum support flexibility and damping of flexible rotors to minimize vibrational amplitudes in the vicinity of the rotor first critical speed. First, the governing equations for the Jeffcott rotor model mounted on flexible supports are derived and the optimal parameters for the supports have been analytically achieved using H∞ and H2 optimization procedures. The approach method of the tuned damper support system is similar to that designed for dynamic vibration absorber optimization. The H∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the rotor amplitudes, as well as, the H2 optimum parameters to minimize the mean square motion of flexible rotor as analytical formulas. It is proven by numerical simulations that the system optimization design can effectively improve the synchronous unbalance response. Comparison of two optimization procedure showed the vibrational amplitudes with H2 optimization was smaller than H∞ one.
