The findings demonstrate that the proposed methodology is
accurate and reliable for estimating the effective damping
introduced by a PTMD on an in-service structure.
Figure 1. Schematic geometry of a PTMD attenuated system
expressed in modal coordinates.
2 THEORETICAL COMPUTATION OF EFFECTIVE
DAMPING
The concept of effective or equivalent damping introduced by
a TMD was first proposed by Vickery [17] and McNamara
[12]. The method seeks to match the mean square
displacement response of the TMD-attenuated system with a
SDOF oscillator operating at the same frequency of the
controlled mode. The damping in the SDOF system is the
effective damping of the attenuated structure. Equations
relating the parameters of the main and auxiliary systems of
the TMD-equipped structure to the effective damping have
been developed for main mass excited [12] and base excited
structures [8] with conventional translational TMDs and
PTMDs. PTMDs are considered herein, but the concepts can
be easily applied to conventional TMDs