Classification of viscoelastic models with integer and fractional order derivatives

Abstract

In the world literature there exists a wide variety of papers devoted to linear viscoelastic models. This work was initiated by the absence of a single generally accepted classification of viscoelastic models. We focused on the basic mechanical models, namely, the Kelvin-Voigt, Maxwell, standard linear solid and Jeffreys models. All other models are different combinations of basic elements connected in series or in parallel. The classification also includes viscoelastic models with fractional derivatives and fractional operators.

Enhancing Structural Vibration Damping in Marine Machinery: A Comprehensive Numerical Investigation with Modal and Harmonic Analysis

“…In the time domain, the Prony series is a frequently used numerical method that accurately represents the connection between the relaxation and creep functions of viscoelastic materials. [37] Researchers often employ this method to model viscoelastic materials, validating their findings through experimental data from various polymeric materials.…”

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

“…Al‐Gharabli et al [15] studied the free vibration analysis of a three‐layer viscoelastic sandwich plate modeled by fractional theory, derived the motion governing equation using Lagrange equations, and obtained the frequency response of sandwich plates by Rayleigh–Ritz method. Krusser and Shitikova [16] used FKV constitutive relation to depict nonlinear vibration of partially viscoelastic polyethylene terephthalate (PET) films under external excitation forces. Abouelregal and Salem [17] tested the thermoviscoelastic vibration of Pasternak‐based viscoelastic microbeams using fractional calculus.…”