Equivalent viscous damping system for viscoelastic fractional derivative model

The viscoelasticities of various polymers have been fitted with viscoelastic fractional derivative models. The time domain response computation was very complex because of the branch analytical functions used in the inverse Laplace transformation. The equivalent linear viscous damping system for the viscoelastic fractional derivative model is discussed here. An equivalent is obtained for the expression of equivalent damping and stiffness for a system with a single degree of freedom. The time domain and frequency domain responses of the original system are compared with the equivalent system for δ excitation and harmonic excitation. The results show little difference between the original and equivalent system response with little damping and narrow bandwidth response. Therefore, for these conditions, the original system can be replaced by the equivalent system with sufficient accuracy but less calculation difficulty.