Second-order analysis of wave propagation in an MEE microbeam using Mindlin-Medick approximation

This paper develops a second-order model of wave propagation in a magneto-electro-elastic (MEE) microbeam, considering the extension, flexure, fundamental shear, thickness-stretch, and symmetric shear deformations, predicted by using Mindlin-Medick approximation and an extended version of modified couple stress theory (MCST). The one-dimensional coupled equations of motion and complete boundary conditions are simultaneously derived on the basis of Hamilton's principle. Based on the newly developed wave equations, the dispersion relations and corresponding wave modes are investigated in transversely isotropic MEE microbeams. Numerical results show that the wave frequencies of the present MEE microbeam model are always larger than those of its classical counterparts under identical wave numbers. The effects of couple stress on the dispersion relation are found to be significant when the microbeam thickness becomes very small. Numerical results also indicate that the magnitude of cutoff frequency is inversely proportional to material size. For the first time, a mathematical explanation is given on the cutoff frequency of high-frequency waves influenced by couple stress effects. An interesting result shows that the cutoff frequency of the symmetric shear is larger than the classical situation and the cutoff frequency of the other two high-frequency branches are equal to classical ones. In particular, relative magnitudes between the cutoff frequency of the thickness-stretch and symmetric shear will change when the beam height reaches a certain value. Finally, a study on wave modes shows the possibilities to optimize the deformed shapes, electric, and magnetic potential distributions in MEE microbeams. These results are beneficial for optimizing the size-dependent properties of MEE microbeams and for designing acoustic wave devices at the microscale.