Comments on "Nonlinear vibration of viscoelastic beams described using fractional order derivatives". (18th August 2018)

• Record Type: Journal Article
• Authors: Lin, R.M.
• Is Part Of: Journal of sound and vibration. Volume 428(2018)
• Page Start: 195
• Page End: 204
• Publication Date: 2018-08-18
• Subjects: Nonlinear vibration -- Fractional derivatives -- Viscoelastic damping -- Modelling of nonlinear vibration; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2018.05.015
• Languages: English
• ISSNs: 0022-460X

Abstract

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.