Post-yield characteristics of magnetorheological fluids; from modelling to large-amplitude vibration analysis of sandwich plates using nonlinear finite element method

Abstract

The present study concerns with post-yield characterization of magnetorheological (MR) fluid and development of a phenomenological model representing the linearized equivalent storage and loss moduli of the fluid in the nonlinear region. It also investigates the nonlinear vibration behaviour of MR based sandwich plates undergoing large amplitude oscillation. To this end, using a magneto-rheometer, the equivalent storage and loss moduli associated with the first harmonic of the measured nonlinear stress-strain data are evaluated under varying shear strain amplitude and magnetic flux intensity. A simple phenomenological model is subsequently proposed to quantify the post-yield moduli of the MR fluid in terms of shear strain magnitude and applied magnetic field. Using the developed model combined with the classical plate theory (CPT), von Karman's formulation and Hamilton's principle, the nonlinear governing equations of motion of the sandwich panel incorporating MR fluid as the core layer have been developed in the finite element form. Displacement control strategy is used to solve the nonlinear equations and identify dynamic characteristics of the structure in terms of natural frequency and loss factor. The results are then compared with those available in literature to validate the developed model. Finally, the developed model has been employed to investigate the effects of post-yield characteristics of the MR fluid, maximum vibration amplitude and applied magnetic field on the nonlinear dynamic characteristics of the MR sandwich panels.