A macroscopic viscoelastic model of magnetorheological elastomer with different initial particle chain orientation angles based on fractional viscoelasticity

2021 ◽  
Author(s):  
Jiahao Fan ◽  
Jianfei Yao ◽  
Yang Yu ◽  
Yan Li
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Properties ◽  
Orientation Angle ◽  
Model Parameters ◽  
Magnetorheological Elastomer ◽  
Initial Particle ◽  
Chain Orientation ◽  
Particle Chain ◽  
Fractional Derivative Model ◽  
Inclination Angles

Abstract In this paper, a macroscopic viscoelastic modeling method for magnetorheological elastomer (MRE) based on fractional derivative model is presented to describe the dynamic viscoelastic properties of MRE with different initial particle chain orientation angles. The angle between the particle chain and the applied magnetic field is used as an indicator to describe the directionality of the particle chain. MRE samples with different initial inclination angles have been designed and fabricated. The dynamic viscoelastic properties of different MRE samples under shear working mode were measured using a parallel plate rheometer. The dynamic viscoelastic properties of MRE with different initial inclination angles are analyzed under the test conditions of different strain amplitude, frequency and magnetic flux density. The test results show that the initial inclination angle of the particle chain in the MRE has significant effect on the dynamic viscoelastic properties of the MRE. A polynomial function is used to describe the relationship between the initial particle chain orientation angle and the magneto-induced modulus of MRE. A phenomenological model of magneto-induced modulus is established based on the fractional derivative model. The model parameters are identified using the nonlinear least square method. The predicted values of the model are in good agreement with the experimental results, indicating that the model can well describe the dynamic viscoelastic properties of MRE.

scholarly journals Challenges in the Application of Fractional Derivative Models in Capturing Solute Transport in Porous Media: Darcy-Scale Fractional Dispersion and the Influence of Medium Properties

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yong Zhang ◽  
Charalambos Papelis ◽  
Michael H. Young ◽  
Markus Berli
Keyword(s):  
Fractional Derivative ◽  
Size Distribution ◽  
Fluid Velocity ◽  
Regional Scale ◽  
Glass Beads ◽  
Model Parameters ◽  
Late Time ◽  
Truncation Parameter ◽  
Fractional Derivative Model ◽  
Segregated Flow

Heterogeneous media consisting of segregated flow regions are fractional-order systems, where the regional-scale anomalous diffusion can be described by the fractional derivative model (FDM). The standard FDM, however, first, cannot characterize the Darcy-scale dispersion through repacked sand columns, and second, the link between medium properties and model parameters remains unknown. To fill these two knowledge gaps, this study applies a tempered fractional derivative model (TFDM) to capture bromide transport through laboratory repacked sand. Column transport experiments are conducted first, where glass beads and silica sand with different diameters are repacked individually. Late-time tails are observed in the breakthrough curves (BTC) of bromide even in relatively homogeneous glass beads. The TFDM can capture the observed subdiffusion, especially the late-time BTC with a transient declining rate. Results also show that both the size distribution of repacked sand and the magnitude of fluid velocity can affect subdiffusion. In particular, a wider sand size distribution or a smaller flow rate can enhance the subdiffusion, leading to a smaller time index and a higher truncation parameter in the TFDM. Therefore, the Darcy-scale dispersion follows the tempered stable law, and the model parameters might be related to the soil size and flow conditions.

Viscoelastic properties of uncured resin composites: Dynamic oscillatory shear test and fractional derivative model

2015 ◽  
Vol 31 (8) ◽  
pp. 1003-1009 ◽  
Author(s):  
Ljubomir M. Petrovic ◽  
Dusan M. Zorica ◽  
Igor Lj Stojanac ◽  
Veljko S. Krstonosic ◽  
Miroslav S. Hadnadjev ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Viscoelastic Properties ◽  
Shear Test ◽  
Oscillatory Shear ◽  
Resin Composites ◽  
Fractional Derivative Model

BAYESIAN CHARACTERIZATION OF FRACTIONAL DERIVATIVE MODEL PARAMETERS OF VISCOELASTIC MATERIALS

2015 ◽  
Author(s):  
Fernanda Oliveira Balbino ◽  
Paulo Justiniano Ribeiro Junior ◽  
Marilda Munaro ◽  
Eduardo Marcio Oliveira Lopes
Keyword(s):  
Fractional Derivative ◽  
Model Parameters ◽  
Viscoelastic Materials ◽  
Fractional Derivative Model

Dynamic Mechanical Properties of Agarose Gels Modeled by a Fractional Derivative Model

2004 ◽  
Vol 126 (5) ◽  
pp. 666-671 ◽  
Author(s):  
Qingshan Chen ◽  
Bela Suki ◽  
Kai-Nan An
Keyword(s):  
Fractional Derivative ◽  
Power Law ◽  
Complex Modulus ◽  
Dynamic Mechanical Properties ◽  
Model Parameters ◽  
Culture Studies ◽  
Agarose Gels ◽  
Dynamic Mechanical ◽  
Fractional Derivative Model ◽  
Power Law Exponent

The complex modulus E* and elastic modulus E′ of agarose gels (2% to 4%) are measured with a dynamic mechanical analyzer in frequency sweep shear sandwich mode between 0.1 and 20 Hz. The data showed that E* and E′ increase with frequency according to a power law which can be described by a fractional derivative model to characterize the dynamic viscoelasticity of the gel. The functions between the model parameters including storage modulus coefficient H and the power law exponent (β) and the agarose concentration are established. A molecular basis for the application of the fractional derivative model to gel polymers is also discussed. Such an approach can be useful in tissue culture studies employing dynamic pressurization or for validation of magnetic resonance elastography.

Variability analysis of vibrational responses in a passenger car considering the uncertainties of elastomers

2015 ◽  
Vol 230 (6) ◽  
pp. 910-927 ◽  
Author(s):  
Jong-Hyun Kwon ◽  
Dooho Lee
Keyword(s):  
Fractional Derivative ◽  
Dynamic Characteristics ◽  
Design Stage ◽  
Model Parameters ◽  
Response Distribution ◽  
Passenger Car ◽  
Operational Conditions ◽  
Variability Analysis ◽  
Vibrational Response ◽  
Fractional Derivative Model

Passenger cars have many elastomeric joints that are used to reduce the vibration transmission from the source to the cabin structure. In the design stage, the dynamic characteristics of the elastomeric joints are optimally determined in order to satisfy the design goals for interior noise and vibration. However, the material properties of the elastomeric joints have large variations due to production variability. In addition, operational conditions, e.g. environmental temperature, vary according to the locations of the car. As a result, the vibrational comfort of a passenger car exhibits large variations. In this paper, the amount of vibration fluctuation due to uncertain elastomeric joint parameters is estimated using a statistical approach. First, the dynamic characteristics of the elastomers are described using the fractional derivative model. The uncertainties of the fractional derivative model parameters of the elastomers are characterized using a statistical calibration approach based on specimen test data. Then, a finite element model for the elastomers and the passenger car structure are constructed in order to calculate the vibrational response. In order to estimate the variability of the vibrational response due to the uncertainties of the elastomers, uncertainty propagation analyses are conducted using the eigenvector dimension reduction (EDR) method. The operational conditions such as temperature are also included in the variability analysis. The performance of the EDR method is assessed through comparing the estimated response distribution with that of the Monte Carlo simulation (MCS) method in a simplified structure. The variability analysis results demonstrate that the vibrational response variation due to the uncertainties of the elastomers can be efficiently predicted using the proposed method. The proposed variability analysis procedure could be an effective tool in the design stage for quality control of passenger car comfort.

Sign in / Sign up

Export Citation Format

Share Document