Finite Element Formulation of a Sandwich Beam with Embedded Electro-Rheological Fluids

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Abstract
In this study, the amplitude-dependent dynamic characteristics of the ER sandwich beam was investigated. The nonlinear constitutive relation of the ER fluid in quasi-static shear was modeled by an exponential function. With the assumed quasi-static model, the hysteresis loop of ER fluid subjected to oscillatory shear strain was constructed. Thereby, the linearized complex moduli of the fluid at different amplitude of strain were derived by an energy approach. With this derived complex moduli, a linear finite element formulation of the sandwich beam structure based on Hamilton's principle was presented first. Then, an iterative process was presented to take the material nonlinearity of the ER fluid into account. The numerical examples of the sandwich beams in different boundary conditions demonstrated that the present modeling predicted qualitatively the changes of resonant frequencies and damping factors with respect to the amplitude of excitation as observed in the literature.