Optimum tuning and damping of a dynamic vibration absorber applied to a force excited and damped primary system

The frequency locus method is summarized and then applied to the optimization of the spring and damper rates for a dynamic vibration absorber. The primary system to which the vibration absorber is attached consists of a force-excited sprung mass with associated viscous damping. The construction of the frequency loci for the overall system leads to the determination of graphical criteria for the optimization, and thence to the discovery of a tuning function which enables the optimal natural frequency for the absorber to be determined. The tuning function can be minimized by numerical methods and the solutions, which depend only on the mass ratio (μ) and primary relative damping rate (ζ1) are presented in the form of a computed family of curves. The optimum relative damping rate (ζ20) for the vibration absorber may be found directly once the optimum tuning frequency has been obtained.