Vibration attenuation of a beam supporting an unbalanced rotor using nonlinear energy sink

摘要

Unbalance in rotating components is very common. Moreover, rotating components input a force to the supporting structure whose amplitude varies quadratically with the rotor speed. As a rotating machine starts from the static condition and approaches to a higher operating speed, it is possible that several modal frequencies of the support beam get excited. Therefore, a vibration mitigation system is required to be efficient at higher operating speeds as well as to provide enough suppression at lower traversing speeds. Here, a nonlinear energy sink (NES) is attached underneath a simply supported beam subjected to the vertical unbalance force component of the rotor. Euler-Bernoulli beam theory is used for the dynamic modeling of the beam along with the Euler-Lagrange equation to get equations of motion of the beam and NES, which are solved numerically. The complexification averaging method is utilized to get the amplitude-frequency response of the system analytically for stability analysis and comparison with the numerical solution. The optimum values of the absorber parameters are obtained utilizing particle swarm optimization. The optimum NES is capable of efficiently reducing vibration amplitude for several modes of beam excited at different rotor speeds. It is found that the NES tuned at the first mode is effective in amplitude reduction for lower to higher operating speed ranges, whereas the NES tuned at the third mode performs better for higher operating speeds. The optimum NES also performs well for a sufficient range of change in the amount of unbalance of the rotor.