Mechanically induced electric and magnetic fields in the bending and symmetric-shear deformations of a microstructure-dependent FG-MEE composite beam

Abstract

A new FG-MEE composite microbeam model is developed using a general higher-order deformation theory (GHDT) to account for the symmetric thickness-shear and thickness-stretch deformations of a beam and a modified couple stress theory (MCST) to describe the microstructure-dependent size effect. Based on the basic assumption of field variables and Hamilton’s principle, the one-dimensional second-order coupled equations of motion and complete boundary conditions are obtained simultaneously. The present coupled equations include the microstructure dependence and higher-order extensions, which can reduce to the size-dependent Bernoulli-Euler, Timoshenko and Mindlin-Medick theories. Static problems of a simply supported beam loaded by uniform loading and a concentrated second-order moment are analytically solved by directly applying the newly developed equations. For the bending case, the numerical results show that the magnitudes of displacement, electric, magnetic, stress, electric displacement and magnetic flux fields are smaller than those predicted by classical theory. In addition, it is found that FG parameter can be used to control the electric and magnetic fields. For the concentrated second-order moment case, a new phenomenon of local electric and magnetic fields are demonstrated in the present FG-MEE composite microbeam structure. These results are useful for theoretically/numerically estimating or designing the MEMS of FG-MEE composites.