Based on the theory of fractional calculus and the spectral theory of vibration, a new spectrally formulated finite element method of analysis is developed which is capable of making accurate predictions of the dynamic response of structures with added dampers. The frequency-dependence 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 element which can be used to model structural dampers. The approach has an advantage over the usual viscous treatment, which appears to lack physical motivation. The nonlinear damping solution is shown graphically, and the consistency of method is investigated. Using a computer program, the proposed formulation has been used to derive the dynamic response of a tall structure with added viscoelastic dampers. Copyright © 1996 Elsevier Science Ltd.
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