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

In this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. This strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. From the best knowledge of author, it is the first time that this theory is used for investigating wave propagation in nanoplates. It is also the first time that magnetic field is considered in modeling the wave propagation in rectangular nanoplates. In this article, an analytical method is adopted to achieve an exact solution for the governing equation. To verify the present methodology, our results are verified with the results published by present authors and other researchers. It is obtained that with the increase of static gradient parameter, the frequencies are increase. It is also shown that the phase velocities increase for the increase of magnetic field.