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A Bingham Flow Model to Predict the Vibrational Damping Characteristics of an Electrorheological Fluid-Filled Annulus.

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Master's thesis,

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The research discussed in this report theoretically and experimentally investigates the dissipation of vibrational energy through the relative shearing within an electrorheological ER fluid contained in an annulus. This work develops a model for both the damping and flow characteristics of an ER fluid due to axial excitation of the flexible structure where it is contained. Based on a creeping Bingham fluid assumption, the model calculates the radial and axial velocity components in the fluid resulting from harmonic excitation. The axial velocity is modeled as one dimensional in the axial direction and the radial velocity as two dimensional in the radial and axial directions. These velocity components are used to formulate the non-Newtonian viscous energy dissipation and calculate the total strain energy for the flexible cylinder containing the fluid. The damping ratio of the ER fluid system is predicted based on the ratio of the dissipated energy to the strain energy. The evaluation of this Bingham fluid model relies on the development of the constitutive relationship for the ER fluid and the electric field activating the fluid. The relationship between the yield stress and the electric fields was accomplished by fitting the Bingham constitutive law to measured shear stress and shear strain rate data for corn- starch and mineral-oil ER fluid. The evaluation of the electric field strength within the fluid was analytically derived using conformal mapping techniques and Jacobian elliptic functions. An attenuation experiment was conducted to compare model damping ratio predictions to a measured system response as a function of the applied electric field. The damping ratio of the ER structure was evaluated from transmissibility experiments and compared to Bingham model predictions.

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  • Electricity and Magnetism
  • Fluid Mechanics

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