Rotating machinery support design with the aim of robustly absorbing transient disturbances over a broad range of frequencies has significant importance regarding the various applications of this machinery. Hence, the nonlinear energy sink may be regarded as an efficient passive absorber, possessing adaptivity to the frequency content of vibrations of the primary system. This paper studies the effect of nonlinear energy sinks on the vibration suppression of a flexible rotor supported by a linear damping and an essentially nonlinear stiffness. First, the governing equations for the Jeffcott rotor model mounted on flexible supports are derived and numerically solved. Then, the optimal parameters for the linear supports have been analytically achieved by H∞ optimization procedure. Numerical simulations have been performed to optimize the nonlinear energy sink parameters by using Matlab software in order to obtain the optimum performance for vibration reduction. Moreover, the H∞ optimum parameters such as tuning frequency and damping ratios are expressed based on fixed-point theory to minimize the rotor amplitudes. It is proven by numerical simulations that the system optimization design can effectively improve the synchronous unbalance response.
