Rotating machinery support design with the aim of reducing the force transmitted to the foundation has significant importance regarding the various applications of this machinery. This article presents H∞ and H2 methods for calculating the optimum support flexibility and damping of flexible rotors to minimize force transmissibility in the vicinity of the rotor’s 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 are analytically achieved by H∞ and H2 optimization procedures. The proposed approach of the tuned damper support system is similar to that designed for dynamic vibration absorber optimization. The main objective of the H∞ optimization is to minimize the force transmitted based on fixed-point theory and the mean square transmissibility of flexible rotor is minimized in the H2 optimization design as analytical formulae. It is proven by numerical solution that the system optimization design can effectively minimize the force transmitted to the foundation. Comparison of two optimization than with H∞.
