On an Integrated Dynamic Characterization of Viscoelastic Materials by Fractional Derivative and GHM Models

Abstract

The passive vibration control of mechanical systems under unwanted vibrations can be accomplished in a very effective way by using devices incorporating viscoelastic materials. The design of such devices requires a broad knowledge of the dynamic properties of the employed viscoelastic material, usually supplied by adequate mathematical models. Among the available mathematical models, the fractional derivative (FD) model and the Golla-Hughes-McTavish (GHM) model, along with either the Williams-Landel-Ferry (WLF) equation or the Arrhenius equation, are now very prominent. The current work investigates the use of these models in a wide and integrated dynamic characterization of a typical and thermorheologically simple viscoelastic material. It focuses on experimental data collected from 0.1 to 100 Hz and-40 °C to 50 °C, which are simultaneously manipulated to raise both the frequency and the temperature dependencies of the material. In fitting the models, a hybrid approach-combining techniques of genetic algorithms and nonlinear optimization-is adopted. The ensuing results are evaluated by means of objective function values, comparative experimental-predicted data plots, and the Akaike's Information Criterion (AIC). It is shown that the four-parameter fractional derivative model presents excellent curve fitting results. As for the GHM model, its modified version is the most adequate, although a higher number of terms is required for a satisfactory goodness-of-fit. None the less the fractional derivative model stands out.

Constitutive Model of Isotropic Magneto-Sensitive Rubber with Amplitude, Frequency, Magnetic and Temperature Dependence under a Continuum Mechanics Basis

“…However, the drawback is that a large number of Maxwell elements are needed to model the viscoelastic behavior of rubber accurately. Research results found that by utilizing a fractional standard linear solid (SLS) model combined with the WLF function, the temperature dependent viscoelasticity of rubber can be depicted more accurately with fewer parameters [ 48 , 49 , 50 , 51 , 52 ]. Therefore, a fractional SLS model with the WLF function is introduced to predict the temperature-dependent viscoelastic behavior of MS rubber in this paper.…”