In the present article, the free vibration analysis of a multi-layer rectangular plate with two magnetorheological (MR) fluid layers and a flexible core is investigated based on exponential shear deformation theory for the first time. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The displacement of the flexible core is modeled using Frostig’s second order model which contains a polynomial with unknown coefficients. MR fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they have the capability to change the stiffness and damping of a structure. The governing equations of motion have been derived using Hamilton`s principle. The Navier technique is employed to solve derived equations. To validate the accuracy of the derived equations, the results in a specific case are compared with available results in the literature, and a good agreement will be observed. Then, the effect of variation of some parameters such as magnetic field intensity, length to width ratio (a/b), length to thickness ratio (a/h), core thickness to panel thickness ratio (h_c/h) and MR layer thickness to panel thickness ratio (h_MR/h) on natural frequency of the sandwich panel is investigated.
