Vibration analysis and optimal design of multi-layer plates partially treated with the MR fluid

The vibration characteristics of a sandwich plate partially treated with the Magneto-Rheological (MR) fluid are investigated numerically and experimentally considering different boundary conditions and intensities of the magnetic flux. A cantilevered sandwich plate consisting of an aluminum host layer with nine equal cavities for the MR fluid treatments and a constraining layer was fabricated for experimental characterizations and validations of the finite-element (FE) model. The dynamic responses of the untreated plate and the partially treated plate, where only one of the nine cavities in the core layer was filled with the MR fluid (MRF 132DG), were measured under harmonic excitation applied at the fixed support. The finite element model of the sandwich plate, developed using the classical plate theory (CPT) and first-order shear deformation theory (FSDT) is verified using the experimental data. The FE model considers the effect of slippage between the top and bottom layers of the structure. The validated FE model is subsequently used to investigate the effects of partial MR fluid treatments, magnetic flux intensity and boundary conditions on the dynamic response characteristics of the structure. The effect of shear deformation on the vibration properties of the MR sandwich plate is further highlighted. Finally, three optimization problems are formulated to identify optimal locations for the MR fluid treatments so as to maximize the variations in the natural frequencies and damping ratios in response to magnetic field. The solution of the optimization problem, attained using the genetic algorithm (GA) suggested that the MR fluid applied to locations with noticeable shear strain can maximize the stiffness variations and damping of the structure, significantly.