A simple new closed form of the Green function for axisymmetric magnetostatic problems is found analytically in cylindrical coordinates. The result is verified by applying several examples.  

This paper investigates the reason behind the low magnetic field computation in cylindrical coordinates using finite difference method, when boundary conditions of the third or fourth kind are used. The same field computation has also been performed using the finite element method but this problem did not occur. It thus, presents a technique to overcome the problem of low magnetic field calculation using finite difference method. The results obtained by the new technique are in close agreement with the finite element method as well as the analytical solution. Finally, an analysis of the possible source of error in modeling magnetostatic boundary conditions in finite difference formulation of vector Poisson or Laplace equation in cylindrical coordinates is performed.

Magneto-electro-elastic materials are multiphase smart materials that exhibit coupling among electrical, magnetic and mechanical energy fields. Due to this ability, they have been the topic of numerous research in the past decade. In this paper, buckling behavior of a multiphase magneto-electro-elastic rectangular plate with simply supported boundary conditions is investigated, based on Reddy’ s higher-order shear deformation theory. Gauss’ s laws for electrostatics and MAGNETOSTATICS are used to model the electric and magnetic behaviors of the plate. The partial differential equations of motion are reduced to ordinary differential equations by using the Galerkin method. Then, the closed-form expression for the critical buckling load of the plate considered is obtained. Some examples are presented to validate the study and to investigate the effects of some parameters on the critical buckling loads of the multiphase magneto-electroelastic rectangular plates. It is found that the buckling behavior of the magneto-electro-elastic plate is dominated by the elastic properties of the plate, and magneto-electric coefficients slightly increase the critical buckling load of the plate.

Vibration response of a two-dimensional magneto-electro-elastic plate is investigated in this paper. The considered multi-phase plate is rectangular and simply-supported resting on an elastic foundation. The plate is under aerodynamic pressure and subjected to temperature change. It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces. The nonlinear vibrational analysis of the described plate is considered as an innovation of the present paper, which had not been done before. To model this problem, third-order shear deformation theory along with Gauss’ s laws for electrostatics and MAGNETOSTATICS, first-order piston theory, and Galerkin and multiple times scale methods are used. After validating the presented method, effects of several parameters on the natural frequency, time history, backbone curve, and phase plane diagram of this smart composite plate are obtained. It is found that for plates with constant a/h ratio, electric and magnetic potentials have noticeable effects on the time histories, phase plane diagrams and backbone curves of the plates with smaller thicknesses. In addition, the numerical results of this research indicate that some parameters have considerable effect on the vibration behavior of presented plate. Elastic parameters of the foundation, applied electric and magnetic potentials, and environment temperature are important parameters in this analysis.