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 (2D) functionally graded materials (FGMs) beams is developed for investigating nonlinear dynamics. It shown that asymmetric modes induced by 2D FGMs may significantly affect dynamic responses, which tremendously different from previous studies. Taking into account geometric nonlinearity, equation motion and associated boundary conditions are derived according to Hamilton’s principle. The natural frequencies numerical calculated generalized differential quadrature method. frequency responses forced vibration constructed based on Galerkin technique incorporating with incremental harmonic balance approach. influences material distributions, length–thickness ratio, electric voltage, magnetic potential as well condition resonant response amplitude discussed in details. notable increasing axial thickness FG indexes, negative positive can lead decline resonance peak, usually applied accurately design multi-ferroic composite structures. Furthermore, characteristics be regulated tuning/tailoring materials.