The selection of optimum absorber parameters is of utmost importance in the case of vibration control by the tuned mass damper (TMD). This paper presents an alternative expression for the optimum tuning ratio of the TMD. It has been derived in closed-form, based on the 'fixed-point' theory of Den Hartog which had been proposed for the case of undamped structural systems. The present expression has the advantage of being applicable for damped structures. The values of the optimum tuning ratio have been derived from the expression proposed in this paper for different structural and damper parameters. These values of optimum tuning ratio have been compared with those obtained from existing theories as well as from those obtained numerically. A simulation study has also been carried out to examine the performance of the optimally designed TMD.

This paper investigates the use of a passive control device, namely, a tuned mass damper (TMD), for the mitigation of vibrations due to the along-wind forced vibration response of a simplified wind turbine.The wind turbine assembly consists of three rotating uniform rotor blades connected to the top of a flexible uniform annular tower, constituting a multi-body dynamic system.First,the free vibration properties of the tower and rotating blades are each obtained separately using a discrete parameter approach, with those of the tower including the presence of a rigid mass at the top, representing the nacelle, and those of the blade including the effects of centrifugal stiffening due to blade rotation and self-weight. Dragbased loading is assumed to act on the rotating blades, in which the phenomenon of rotationally sampled wind turbulence is included. Blade response time histories are obtained using the mode acceleration method, allowing base shear forces due to flapping motion for the three blades to be calculated. The resultant base shear is imparted into the top of the tower. Wind drag loading on the tower is also considered, and includes Davenport-type spatial coherence information. The tower/nacelle is then coupled with the rotating blades by combining their equations of motion. A TMD is placed at the top of the tower, and when added to the formulation, a Fourier transform approach allows for the solution of the displacement at the top of the tower under compatibility of response conditions. An inverse Fourier transform of this frequency domain response yields the response time history of the coupled blades/tower/damper system. A numerical example is included to qualitatively investigate the influence of the damper. Figure 4. Transfer function for the coupled tower/nacelle and rotating blades model (Ω = 15 rev min -1 ) including and excluding the TMD 314 P. J. Murtagh et al.Figure 7. Simulated displacement response at the top of the tower coupled tower/nacelle and rotating blades model (Ω = 30 rev min -1 ) including and excluding the TMD 316 P. J. Murtagh et al.

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