DESIGN CRITERIA AND LOADS
Barry J. Vickery, Jon K. Galsworthy and Rafik Gerges
Tuned mass dampers have been used to add damping to structural and mechanical systems for many years and the theory of their design and behaviour when subjected to sinusoidal forcing has been elegantly described by Den Hartog (1956). The optimization of these dampers with linear dashpots and springs and for sinusoidal excitation is well treated by Den Hartog but considerably less attention has been paid to non-linear devices on systems subject to the random loads imposed by the wind acting on tall buildings and other slender structures such as towers and chimneys.
The present paper deals with the behaviour of non-linear T.M.D.'s subject to random Gaussian excitation. Attention is limited to two simple non-linear forms that occur commonly in practice. These two forms are dry-friction or constant force dampers and "velocity squared" or V2 damping associated with, for example, flow through an orifice or flow in a rough pipe. Although there is some mathematical development, this is not the essential part of the paper. The prime intention of the paper is to examine the more general characteristics of these non-linear dampers with a view to assessing the advantages and disadvantages of each compared to linear T.M.D.'s.
The characteristics of linear T.M.D.'s are reviewed briefly in Section 2 which includes sample design charts for linear systems. Linearization of the simple friction and V2 T.M.D.'s is treated in Section 3. The characteristics of non-linear as opposed to linear T.M.D.'s is also addressed in Section 3. Section 4 presents some numerical results and designs for non-linear T.M.D.'s for a fictitious building.
A linear T.M.D. is shown schematically in Fig. 1. The values of M, K and C define the primary system ie the building or tower in question while the values of m, k and c define the T.M.D. The value of the primary mass is a function of the mass and mass distribution of the building, the mode shape under consideration and the modal deflection at the point of attachment of the T.M.D.