A FRACTIONAL-SPECTRAL METHOD FOR VIBRATION OF DAMPED SPACE STRUCTURES

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.