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

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.

The Comparison of Fractional Derivative Model and Classical Spring-Dashpot Model in the Identification of Viscoelastic Characteristics of a Rubber Material

In the design of viscoelastic materials used in rubber products, not theoretical approaches but experimental approaches have been usually employed. This is due to the difficulties in mathematical procedures of the dynamic material characteristics such as the dependencies of strain amplitude, frequency and/or environmental temperature in deformation. In mathematical approach there are two kind of analytical models for a complex module of the material, which are a fractional derivative model and a spring-dashpot model. However there are few papers dealing with the study of the identifications of parameters for the experimental modulus actually obtained not only by using the fractional derivative model but also by using the spring-dashpot model and the discussion of the comparisons of the two models. In the present paper, the complex elastic modulus for a rubber material are obtained experimentally for a wide range of excitation frequency, and the modulus-frequency relations are derived analytically by using the two models, respectively. Finally, the applicability of the models are discussed from the numerical results.

Transient Dynamic Analysis of Unconstrained Layer Damping Beams Characterized by a Fractional Derivative Model

This paper presents a numerical analysis of the influence of mechanical properties and the thickness of viscoelastic materials on the transient dynamic behavior of free layer damping beams. Specifically, the beams consist of cantilever metal sheets with surface viscoelastic treatment, and two different configurations are analyzed: symmetric and asymmetric. The viscoelastic material is characterized by a five-parameter fractional derivative model, which requires specific numerical methods to solve for the transverse displacement of the free edge of the beam when a load is applied. Concretely, a homogenized finite element formulation is performed to reduce computation time, and the Newmark method is applied together with the Grünwald–Letnikov method to accomplish the time discretization of the fractional derivative equations. Amplitudes and response time are evaluated to study the transient dynamic behavior and results indicate that, in general, asymmetrical configurations present more vibration attenuation than the symmetrical ones. Additionally, it is deduced that a compromise between response time and amplitudes has to be reached, and in addition, the most influential parameters have been determined to achieve greater vibration reduction.

Consolidation of Viscoelastic Soil With Vertical Drains for Continuous Drainage Boundary Conditions Incorporating a Fractional Derivative Model

In geotechnical engineering, vertical drainage is the most economical method for accelerating the consolidation of a large area of soft ground. In this study, we analyze the viscoelasticity of the soil and the actual drainage conditions on the top surface of the soil, and then we introduce continuous drainage boundary conditions and adopt a fractional derivative model to describe the viscoelasticity of the soil. With the use of a viscoelasticity model, the governing partial differential equation for vertical drains under continuous drainage boundary conditions is obtained. With the application of the Crump numerical inversion method, the consolidation solution for vertical drains is also obtained. Further, the rationality of the proposed solution is verified by several examples. Moreover, some examples are provided to discuss the influence of interface drainage parameters on the top surface of soil and the viscoelasticity parameters of soil on the consolidation behavior of vertical drains. The proposed method can be applied in the fields of transport engineering to predict the consolidation settlement of a foundation reinforced by vertical drains.

Prediction of Beyond Design and Residual Performances of Viscoelastic Dampers by a Simplified Fractional Derivative Model

When subjected to excessive shear deformation, viscoelastic (VE) dampers may inevitably suffer from damages, due to their VE material layers with limited thickness. Under the circumstance, their stiffness and energy dissipation capabilities may deteriorate but not totally vanish. To estimate the seismic performances of viscoelastically damped structures, the beyond design and residual performances of damaged VE dampers are crucial to protect structures from severe failure during the following main shock or aftershocks. On the other hand, for new viscoelastically damped structures under the normal design earthquakes, neglecting the residual performance of damaged VE dampers may result in nonconservative design. Thus, this study aims to provide approaches to analytically characterize the beyond design and residual performances of damaged full-scale VE dampers. Based on the simplified fractional derivative model, the analytical predictions have been compared with the experimental results. The proposed model works well for the design performance of the intact full-scale VE dampers. Particularly, it can also reproduce the beyond design and residual performances of damaged full-scale VE dampers, if due consideration is taken of the effects of excitation frequencies, ambient temperatures, temperature rises, softening, and hardening.

Identification of Viscoelastic Property of Pile-Soil Interactions with Fractional Derivative Model

The viscoelastic property of pile-soil interactions is modeled by fractional derivative method and is used to characterize the structural dynamics of pile and rheological behavior of a thawing frozen soil. A study of the thawing frozen soil impacts on pile structure’s dynamic characteristic is carried out. The frequency spectrum analysis and empirical modal decomposition are used to identify the pile structure dynamic properties. The rocking mode vibration in which pile behaviors like rigid body supported by viscoelastic soil is extracted to capture the viscoelastic property of pile-soil interactions. The rocking mode exhibiting time-varying frequency features is modeled with fractional derivative model and the fractional derivative order is identified. This study proposes a quick and reliable method to identify the viscoelastic property of pile-soil interactions.