Comments on "Nonlinear vibration of viscoelastic beams described using fractional order derivatives". (18th August 2018) - Lin, R.M.
Abstract: This discussion seeks to address some of the inconsistencies and concerns regarding fractional derivatives when applied to vibration analysis of viscoelastically damped beams [1]. Detailed numerical assessments of the major fractional derivatives of concern have been carried out with their relationships numerically examined. Numerical results have shown that two of the key equations of [1] are mathematically inappropriate and their applications could lead to serious modelling errors. A simplified yet representative nonlinear system with fractional viscoelastic damping and cubic stiffness nonlinearity is used to illustrate the existence of periodic steady-state solutions, as well as amplitude frequency characteristics of such fractional nonlinear systems.