Control of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic plates

• Control of nonlinear vibrations of functionally graded magnet-electro-elastic plates.
• Active constrained layer damping treatment is used.
• Three dimensional nonlinear finite element model is developed.
• GHM method is implemented for passive damping of nonlinear vibrations
• For optimum control top and bottom surfaces of the plates should be magnetostrictive rich material.

This article deals with the analysis of active damping of geometrically nonlinear vibrations of functionally graded magneto-electro-elastic (FGMEE) plates integrated with the patches of the active constrained layer damping (ACLD) treatment. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1–3 piezoelectric composite (PZC). The constrained viscoelastic layer of the ACLD treatment is modeled by using a Golla–Hughes–McTavish (GHM) method in time domain. The material properties of the FGMEE plate are assumed to be functionally graded along the thickness direction according to a simple power-law distribution. Based on the layer-wise shear deformation theory, a three-dimensional finite element (FE) model of the overall smart FGMEE plate has been developed taking into account the effects of coupling between elasticity, electric and magnetic fields, while the von Kármán type nonlinear strain displacement relations are used for incorporating the geometric nonlinearity. Influence of the variation of the power law index, material gradation, edge boundary conditions and the piezoelectric fiber orientation angle in the 1–3 PZC constraining layer of the ACLD treatment on the control of geometrically nonlinear vibrations of the FGMEE plates have been investigated.