Calculation of the optimal parameters of dynamic vibration absorber in consideration of the damper of primary vibration system

The dynamic vibration absorber widely used in machinery and structure vibration passive control is designed on the basis of the fixed point theory. This theory is an approximation because the damper of the primary system is neglected and the fixed point is not coinciding with the resonance point on the amplitude-frequency curve of the primary system which caused by using the arithmetical mean value of damper. In this paper, a two degree of freedom dynamic model for the primary system with a vibration absorber is established in consideration of the damper of the primary system. The frequency ratio (the natural frequency ratio of the absorber to the primary system) and the damping ratio of the absorber are calculated numerically and their optimal values are obtained in the condition of making two maximal values in the amplitude-frequency curve of the primary system be equal and minimum. In addition, their variety laws are analyzed. The analytic equations which describe the relations among the optimal frequency ratio, the optimal damping ratio and the maximal values in the amplitude-frequency curve are derived to testify the reliability of the optimal parameters. The conclusions can provide a practical basis for optimal parameters design of the dynamic vibration absorber.