Wave Propagation in Rectangular Nanoplates Based on Strain Gradient Elasticity Theory and Considering in-Plane Magnetic Field

Through strain gradient elasticity theory, this paper has studies wave propagation in rectangular nanoplates by considering in-plane magnetic field. The strain gradient theory has two gradient parameters and has the ability to be compared with the nonlocal elasticity theory. To the best of the authorsʹ knowledge, this theory has been used for the first time in order to investigate the wave propagation in nanoplates. Moreover, It is the first time that magnetic field has been considered in modeling the wave propagation in rectangular nanoplates. An analytical method is adopted to achieve a closed-form solution for the governing equation. To verify the present methodology, the results are compared with othersʹ findings. It is obtained that with the increase in static gradient parameter, the frequencies have been increased. Furthermore, it is shown that the phase velocities increase for the increase of magnetic field.