Analytical determination of equivalent modal damping ratios of a composite tower in wind-induced vibrations

We present two methods to determine the equivalent modal damping ratios of a composite tower under wind-induced vibrations. Different damping characteristics arise from the construction of the tower with two materials; for the lower main part, say of reinforced concrete and an upper part, say of steel. The first method employs a detailed numerical integration procedure in which the static condensed stiffness matrices are established by the transfer matrix method. The damping matrices of the upper and the lower substructures are modelled with the Rayleigh damping formulation. The second method makes use of a simplified approximation of two lumped masses. Computation using the two methods is demonstrated with a numerical example for a composite T.V. tower of a total height 459 m. Results show that, while the detailed method gives good accuracy but demands intensive computation, the approximate method involves simple calculations and produces data of enough precision for engineering applications.