Based on the theory of fractional calculus and the spectral theory of
vibration, a new spectrally formulated finite element method of analys
is is developed which is capable of making accurate predictions of the
dynamic response of structures with added dampers. The frequency-depe
ndence damping characteristic of structural materials can be modelled
accurately using the fractional derivative model. It is shown that the
proposed method can be extended to develop a nonlinear damping elemen
t which can be used to model structural dampers. The approach has an a
dvantage over the usual viscous treatment, which appears to lack physi
cal motivation. The nonlinear damping solution is shown graphically, a
nd the consistency of method is investigated. Using a computer program
, the proposed formulation has been used to derive the dynamic respons
e of a tall structure with added viscoelastic dampers. Copyright (C) 1
996 Elsevier Science Ltd.