Investigating Vibratory Behavior of Nonlinear Single Unit Impact Dampers Using Perturbation Method and Genetic Algorithm

Abstract

Applications of impact damper to reduce machine tools vibration have been investigated analytically, numerically, and experimentally for many years. The reason for this interest lies in the fact that impacts occur very often in many modern technical devices. In different applications, optimal values of impact damper parameters (impact mass, elastic coefficient of barrier etc.) should be found in order to damp vibrations efficiently. We investigate the predictions of a mathematical model for an impact damper consisting of a pendulum and an elastic barrier. Our model incorporates Hertzian contact between the spherical steel pendulum and the barrier. In next step, due to the strong non-linearity of the model, Homotopy Perturbation and iteration perturbation are used to solve the dynamics equation. Homotopy and iteration perturbation method provide analytical solution for strong non-linear equation. To confirm the accuracy of this method, results are compared with numerical solutions in SimMechanics toolbox of MATLAB. Next, a systematic approach based on a Genetic Algorithm optimization method is used to determine the best design parameters for suppressing vibrations. Finally, optimum parameters for complete quenching of vibrations are obtained.