Frequency Analysis of the Tuned Mass Damper

Abstract

The damping properties of the viscous tuned mass damper are characterized by dynamic amplification analysis as well as identification of the locus of the complex natural frequencies. Optimal damping is identified by a combined analysis of the dynamic amplification of the motion of the structural mass as well as the relative motion of the damper mass. The resulting optimal damper parameter is about 15% higher than the classic value, and results in improved properties for the motion of the damper mass. The free vibration properties are characterized by analyzing the locus of the natural frequencies in the complex plane. It is demonstrated that for optimal frequency tuning the damping ratio of both vibration modes are equal and approximately half the damping ratio of the applied damper, when the damping is below a critical value corresponding to a bifurcation point. This limiting value corresponds to maximum modal damping and serves as an upper limit for damping to be applied in practice.

Optimisation of dynamic vibration absorbers to minimise kinetic energy and maximise internal power dissipation

“…Asami et al [11] attribute this result in Table 1 to Yamaguchi in 1988 [14], although the same criterion was also considered by Miller and Crawley in 1985 [15]. Krenk in 2005 [16] proposed a further method to tune the parameters of a DVA. He tuned the frequency ratio of the two decoupled oscillators using the same criterion proposed by Omondroyd and den Hartog [12] and proposed a new criterion for the optimal damping ratio.…”

Balanced calibration of resonant piezoelectric RL shunts with quasi-static background flexibility correction

“…However, for the classic tuned mass absorber the fixed point frequency calibration is equivalent to equal damping in the two modes associated with the targeted vibration form, as demonstrated by Krenk [26]. Furthermore, the device damping is calibrated to provide an optimal combination of response reduction of the structure and limited absorber motion.…”

Resonant passive–active vibration absorber with integrated force feedback control

“…The classic concept is that of the mechanical tuned mass damper [1,2] shown in Fig. 1(b), in which the absorber mass is suspended to the flexible structure via a spring and a viscous damper.…”

“…An inertia-based absorber equivalent to a tuned mass or inerter damper [1,2,6] and a stiffnessbased absorber similar to that of piezoelectric RL shunt damping [9,10]. Numerical examples demonstrate the efficiency of the two resonant absorber formats when compared to the optimally tuned viscous damper.…”