Vibration attenuation of a continuous rotor-blisk-journal bearing system employing smooth nonlinear energy sinks

Abstract The current paper investigates the effects of a number of smooth nonlinear energy sinks (NESs) located on the disk and bearings on the vibration attenuation of a rotor-blisk-journal bearing system under excitation of a mass eccentricity force. The blade and rotor are modeled using the Euler-Bernoulli beam theory. The nonlinear energy sinks on the bearing have a linear damping and an essentially nonlinear stiffness. The nonlinear energy sinks on the disk have a linear damping, linear stiffness, and an essentially nonlinear stiffness. It can be seen that the linear stiffness of the NESs on the disk is eliminated by the negative stiffness induced by the centrifugal force, and the collection of the NESs can be tuned to a required rotational speed of the rotor by varying the linear stiffness of the NESs. Furthermore, the remained stiffness of the NESs on the disk after elimination of their linear stiffness, would be essentially a nonlinear (nonlinearizable) one. Two nonlinear energy sinks in the vertical axes are positioned on the bearing housing and n n d NESs are located on the perimeter of the disk. The equations of motion are extracted using the extended Hamilton principle. The modal coordinates and complex transformations are employed to decrease the number of equations of motion. A genetic algorithm is used to optimize the parameters of the nonlinear energy sinks and its objective function is considered as minimizing the vibration of the rotating system within an operating speed range. In order to examine the periodic and non-periodic solutions of the system, time history, bifurcation diagram, Poincare map, phase portrait, Lyapunov exponent, and power spectra analyses are performed. System shows periodic and quasi-periodic motions for different values of the system parameters. It is shown that the NESs on the disk and bearings have almost local effects on vibration reduction of rotating system. In addition, the optimum NESs remove the instability region from the system response completely.