Vibration Response of Sandwich Beam with Viscoelastic Core and FGM Face Sheets Using Finite Element Method

The present work explains about the vibration response of a viscoelastic sandwich beam with functionally graded material constraining layers. These layers are formed by varying the ceramic (Al₂O₃) and stainless steel (SUS304) composition along the thinness direction. The basic kinematics is considered from Timoshenko beam theory due to inertia effect. The sandwich beam is formulated. Three-layered sandwich beam is modelled using the finite element method. The top and bottom layers are FGM layers and the middle layer as a viscoelastic core. The linear displacement field is assumed to model the FGM layers and also the core layer displacement field as non-linear. Hamilton’s principle is used to derive the governing equation of motion of the viscoelastic sandwich beam. The vibration analysis has been carried out by using the derived governing equation of motion with cantilever and fixed–fixed boundary conditions. The obtained results are compared with the available literature results. The natural frequencies are calculated with different boundary conditions by varying the core thickness. The influence of core thickness and FGM constraining layer index value on natural frequencies are observed.