The damping of the dynamic vibration absorber

The design parameters of the dynamic vibration absorber notably affect the motion space of the main system. A complete new universal method of attaining the explicit exact solution to the optimum damping was proposed to enhance the accuracy of calculating the dynamic vibration absorber's parameters. The interaction between the main system and dynamic vibration absorber taken into account, many exact analytic solutions, for example displacement amplitude amplification factor, stiffness ratio, fixed point coordinate, optimum damping ratio, and phase angle difference, were investigated with the real number form of differential equation of load motion and using L'Hospital first rule in minute detail. Some characteristic parameters of both the main system and dynamic vibration absorber were gotten. The mechanism of the dynamic vibration absorber was analyzed by comparing the displacement amplitude amplification factor between the dynamic vibration absorber and main system. Generally speaking, the dynamic vibration absorber lags behind the main system by certain degrees. The fixed point theory essentially achieves the extreme large value, but not the maximum value, which is a natural shortcoming required to be overcome. The maximum value of the displacement amplitude amplification factor was acquired adopting MATLAB® Version 7.9.0.529 (R2009b). The relative error between the extreme large value and maximum value increases with the increase in the mass ratio. The relative error between the extreme large value and maximum value is 1.3018-10.397% for the optimum damping ratio. The present solutions would be useful to realize and control the precise dynamic characteristics of the main system and dynamic vibration absorber in practice.