Identifying Mechanical Properties of Viscoelastic Materials in Time Domain Using the Fractional Zener Model

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.

Section: Fractional Derivative (Fd) Modelmentioning

confidence: 99%

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

Júnior

Préve

Balbino

et al. 2019

“…Furthermore, some recent studies about viscoelasticity present developments related to the use of fractional derivatives to obtain simpler rheological models and with a more precise representation of the complex behavior of real materials, such as composite materials, polymeric materials, biological tissues, among others (Bahraini et al, 2013;Pérez Zerpa et al, 2015;Ciniello et al, 2017;Borges et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Modeling the creep behavior of GRFP truss structures with Positional Finite Element Method

Rabelo

Becho

Greco

et al. 2018

This paper presents the development of a formulation, based on Positional Finite Element Method, to describe the viscoelastic mechanical behavior of space trusses. The numerical method used was chosen due to its efficiency in the applications concerning nonlinear numerical analyses. The formulation describes the positional variation over time under constant stress state (creep). The objective is to provide a way to quantify the creep behavior for space truss structures and thus contribute to the encouragement of GFRP usage in such structural components. Time-dependent behavior of such materials is one the most important factors for their use in design of structures, demanding studies about the deformations expected within the operational life of the structural systems. To perform this study, the proposed methodology considers a standard solid rheological model to describe stress-strain time-dependent law. This model is implemented in the formulation for quantify the total strain energy. The effects of the model parameters in the mechanical response of the structure with accentuated geometric nonlinearity were presented. In this analysis, it was possible to identify the influence of the elastic and the viscous moduli on the creep response. Model calibration was performed using test data obtained from literature and a GFRP transmission line tower cross-arm was simulated to predict the evolution of displacements under real operational loads. From the results, it was possible to observe a fast evolution of displacements due to the creep effect in the first 7,500 h. This increase was close to 0.6% in relation to the displacement obtained in the elastic behavior. The presented methodology provided a simple and efficient way to quantify the creep phenomenon in viscoelastic GFRP composites truss structures, as can be seen in the developed analyses.

“…Thus, the mechanical model differential equation, written in terms of integer order derivatives, is replaced by an equation involving fractional derivatives. According to Glöckle and Nonnenmacher (1994), Galucio et al (2004), Mainardi (2010), Rouleau et al (2015) and Ciniello et al (2016), there are several constitutive models involving fractional order derivatives: Maxwell, Kelvin-Voigt, Zener etc.. As presented by Mainardi and Spada (2011) and Ciniello et al (2016), the Zener fractional model ( Figure 1) proves to be fairly efficient in predicting the behavior of linear VEMs. Bagley and Torvik (1986), Galucio et al (2004) and Mainardi (2010) show that the fractional order differential equation that governs the fractional Zener physical system (Figure 1) may be written as…”

Section: Introductionmentioning

confidence: 99%

“…In SI, the units of E b and E  are, respectively, s  and MPa . In general, during the identification of VEMs, several works find proper adjustments when Espíndola et al, 2006;Agirre and Elejabarrieta, 2010;Guedes, 2011;Ciniello et al, 2016;Chen et al, 2017;Sousa et al, 2017). , and strains, ( ) t  , in pure shear tests.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Indirect Identification of the Complex Poisson's Ratio in Fractional Viscoelasticity

Sousa

Silva

Pereira

2018

Self Cite

The use of viscoelastic materials (VEMs) has becoming more and more frequent both as vibration control in general or as parts of structural components. In all applications, the mechanical behavior of such materials can be predicted by the complex moduli (Young's, shear or volumetric) and the complex Poisson's ratio. Over recent decades, various methodologies have been presented aiming at characterizing complex moduli. On the other hand, the indirect identification of the Poisson's ratio, in the frequency domain, proves to be underexplored. The present paper discusses two computational methodologies in order to obtain, indirectly, the complex Poisson's ratio in linear and thermorheologically simple solid VEMs. The first of them uses a traditional methodology, which individually identifies the complex Young's and the shear moduli and, from them, one obtains the complex Poisson's ratio. The second methodologyproposed in the present paper and called 'integrated'-obtains the complex Poisson's ratio through a simultaneous identification of those two complex moduli. Both methodologies start from a set of experimental points of the complex moduli in the frequency domain, carried out at different temperatures. From those points, a hybrid optimization technique is applied (Genetic Algorithms and Non-Linear Programming) in order to obtain the parameters of the constitutive models for the VEM under analysis. For the experiments described here, the integrated methodology proves to be very promising and with a great application potential.