A new analytical approach for axisymmetric free vibration of circular magnetorheological fluid sandwich plate

An exact closed-form solution was introduced to analyze axisymmetric free damped vibration of circular magnetorheological fluid (MRF) sandwich plate. Hamilton principle, as well as the classical thin plate theory were used to extract three fully coupled governing equations of motion and the corresponding boundary conditions. Shear modulus of the MRF was tunable by changing a magnetic field which was perpendicular to the mid-plane of the plate. Using two new functions named as phase and anti-phase in-plane displacement functions (PIDF and AIDF), transverse displacement of the sandwich plate was firstly decoupled and finally, in-plane displacements of the top and bottom layers were extracted to obtain the frequency equation for clamped, simply supported and free boundary conditions. Accuracy and stability of results were assessed according to a finite element analysis. The role of various parameters on variations of natural frequencies and loss factors was investigated. Considering obtained results, it was found that despite the insensitivity of natural frequencies to the intensity of the magnetic field and the MRF thickness variations, the loss factors showed high sensitivity to these parameters. Also, the slope of the plate has a significant role in the dissipated energy of the sandwich circular plate. These findings can be applied by engineers and researchers in designing magnetically controlled devices such as brakes or clutches and heavy motor dampers.