Experimental and modeling of the translation stiffness of magnetorheological elastomer

Abstract

Magnetorheological elastomer is a potential resilient element to meet the vibration mitigation demands of a dynamic system over broad-band frequency. It comprises of ferromagnetic fillers dispersed in a non-magnetic elastomer matrix. Under the influence of an external magnetic field, these fillers readily interact and modify the properties of Magnetorheological elastomer. The response of magnetorheological elastomer under dynamic loading includes the contributions from the viscoelastic properties of matrix and the field sensitive characteristics of the filler. These properties are unique for a particular combination of matrix and the filler. The properties of Magnetorheological elastomer are sensitive to the changes in the operating parameters such as frequency and displacement amplitudes. This demands a large number of experiments to characterize the viscoelastic properties of Magnetorheological elastomer. On the contrary, the overall process of dynamic characterization is simplified by adopting a phenomenological modeling approaches based on the theory of linear viscoelasticity. It is important that the model should be able to represent viscoelastic behavior over wide frequency range in a simple form. The present study is focused on modeling the translation stiffness to realize the concept Magnetorheological elastomer as boundary support damping applications. The dynamic tests are performed on Magnetorheological elastomer under shear mode (volume preserving deformation state) according to the dynamic blocked transfer stiffness method. The viscoelastic properties are evaluated at different frequency, magnetic field and strain amplitudes. These properties are expressed in terms of dynamic stiffness, and the loss factor evaluated from the force-displacement hysteresis loops. The test results indicated that the properties of Magnetorheological elastomer enhanced with an increase in magnetic field and the frequency. The magnetic field dependency is more pronounced compared to frequency. At larger values of frequency and magnetic field, the viscoelastic properties are saturated. For the tested MRE samples, the saturation behavior is observed at 50 Hz and 0.3 T. With an increase in strain the viscoelastic behavior of Magnetorheological elastomer changes from linear to nonlinear. Under magnetized state, the nonlinear behavior occurs at lower strain levels as the matrix-filler frictional energy dissipation isiv intensified. In addition, Magnetorheological elastomer exhibits the Payne effect with the variation in input strain amplitude. The Payne effect is more pronounced under non-magnetized state and it diminished under magnetized state due to the contribution from the filler –filler interactions. The material behavior of Magnetorheological elastomer is modeled by adopting the phenomenological models based on the viscoelastic constitutive relations. In the present study, integer and fractional order derivative based viscoelastic constitutive relations are used. Integer order based model comprises of six parameters, and the fractional order model are represented by five parameters. The parameters of the model are identified by minimizing the error between the response of the model and dynamic compression (translation) test data. Performance of the model is evaluated with respect to the optimized parameters estimated at different sets of regularly spaced arbitrary input frequencies. A linear and quadratic interpolation function is chosen to generalize the variation of parameters with respect to the magnetic field and frequency. The predicted response of the model revealed that the fractional order element model describes the properties of magnetorheological elastomer in a simpler form with reduced number of parameters. The fractional order based model has a greater control over the real and imaginary part of the complex stiffness, which facilitates in choosing a better interpolating function to improve the accuracy of the model. Furthermore, it is confirmed that the realistic assessment of the model performance is based on its ability to reproduce the results obtained from optimized parameters. The material models based on the viscoelastic constitutive relations are not adequate to describe the amplitude dependent characteristics. These attributes are incorporated in the model by adding a linearized Bouc-Wen element. The proposed model comprised of eight parameters, which are identified by minimizing the least square error between the model predicted and the experimental response. The variations of each parameter with respect to the operating conditions are represented by a generalized expression. The parameters estimated from the generalized expression are used to assess the ability of the model in describing the dynamic response of Magnetorheological elastomer. The proposed model effectively predicted the stiffness characteristics with an accuracy, more than 94.3% and the correspondingv accuracy in predicting the damping characteristic is above 90.1%. This model is capable of fitting the experimental value with a fitness value of more than 93.22%.