A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates

A modified Pagano method is developed for the three-dimensional (3D) dynamic responses of simply supported, multilayered and functionally graded (FG) magneto-electro-elastic plates with three different lateral surface conditions. Either the free electric/magnetic potential or the free electric/magnetic flux conditions is prescribed on each lateral surface. The material properties of FG plates are regarded as heterogeneous through the thickness coordinate and then specified to obey a power-law distribution of the volume fractions of the constituents. The Pagano method is modified for the present analysis in that a displacement-based formulation is replaced by a mixed formulation, the complex-valued solutions of the system equations are transferred to the real-valued solutions, a method of propagator matrix is developed for the present method, and a successive approximation (SA) method is used to make the present method feasible for the coupled analysis of FG plates. In the illustrative examples, the influence of the power-law exponent on the natural frequencies of the FG magneto-electro-elastic plates and their corresponding modal variables in the magnetic, electric and elastic fields through the thickness of the plates is studied. The present modified Pagano method combined with the SA method is capable of efficiently approximating the available 3D solutions of FG plates to any desired accuracy.