This paper reports on the numerical results that are performed with a freely vibrating magnetorheological elastomer sandwich beams reinforced by carbon nanotubes, exposed to an angular velocity and a magnetic field. The shear deformable beam model of the Timoshenko is employed to model the top and bottom functionally graded carbon nanotube reinforced (FGCNTR) layers, whereas a linear viscoelastic behavior is considered for the magnetorheological elastomer core layer. Using the Hamilton principle as well as a differential quadrature method, the natural frequencies and corresponding loss factors are derived. Convergence study and comparison results with the literature show a high stability and accuracy of the present approach. Enhancement of angular velocity causes a significant increasing and decreasing trends for the natural frequencies and loss factors, respectively. Observations reveal that there is an optimum value for the magnetic field intensity in which the loss factor is the maximum. Also, the effects of carbon nanotube distributions and geometric parameters of the magnetorheological elastomer and FGCNTR layers on the modal parameters are examined.
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