vibration analysis of sandwich beams with magnetorheological elastomer core and fgm graphene nanoplatelet-reinforced polymer faces on viscoelastic foundation

This study investigates the free vibrations of a sandwich beam with a magneto-rheological elastomer (mre) core reinforced with carbon nanotubes (cnts) and polymer facings reinforced with graphene nanoplatelets (gnps) resting on a viscoelastic foundation. to enhance the accuracy of the results, the modeling of the core and facings of the beam is based on the timoshenko beam model, and the viscoelastic foundation is based on the visco-pasternack model. the governing equations and boundary conditions are derived using hamilton’s principle and solved using navier’s method. after validation, the effects of beam parameters, including the applied magnetic field intensity, core and facing thicknesses, volume fraction of cnts added to the core, volume fraction and distribution pattern of gnps added to the facings, and foundation parameters, on the natural frequencies of the beam in different vibration modes are investigated. the results show that if the goal is to maximize the natural frequencies of the beam, adding gnps to the polymer facings of the beam is significantly more effective than adding cnts to the mre core or increasing the applied magnetic field intensity to the core. the results of this research can be used in the design of sensors and actuators in many industries.