Magneto Electro Elastic Modelling and Nonlinear Vibration Analysis of Bi Directional Functionally Graded Beams

In the paper, a novel magneto electro elastic ( model of bi-directional ( 2 D) functionally graded material s (FGM s ) beam s is developed for investigating the nonlinear dynamics It is shown that the asymmetric modes induced by the 2D FGM s may significantly affect the nonlinear dynamic responses which is tremendously different from previous studies Taking into account the geometric nonlinearity, the nonlinear equation of motion and associated boundary conditions for the beam s are derived according to the Hamilton’s principle The linear frequencies and modes of the beam s are numerically calculated by the generalized differential quadrature method (GDQM) GDQM). The frequency responses of the nonlinear forced vibration are constructed based on the Galerkin technique incorporating with the incremental harmonic balance (I HB) approach. The influences of the material distributions, length thickness ratio, electric voltage, magnetic potential as well as boundary condition on the nonlinear resonant frequency and response amplitude are discussed in details. It is notable that increasing in the axial and thickness FG indexes, negative electric potential and positive magnetic potential can lead to decline the nonlinear resonance frequency and amplitude peak which is usually applied to accurately design the multiferroic composite structures.