Study of terahertz wave propagation properties in nanoplates with surface and small-scale effects

In macroscopic and even microscopic structural elements, surface effects can be neglected and classical theories are sufficient. As the structural size decreases towards the nanoscale regime, the surface-to-bulk energy ratio increases and surface effects must be taken into account. In the present work, the terahertz wave dispersion characteristics of a nanoplate are studied with consideration of the surface effects as well as the nonlocal small-scale effects. Nonlocal elasticity theory of plate is used to derive the general differential equation based on equilibrium approach to include those scale effects. Scale and surface property dependent wave characteristic equations are obtained via spectral analysis. For the present study the material properties of an anodic alumina with crystallographic of 〈 111 〉 direction are considered. The present analysis shows that the effect of surface properties on the flexural waves of nanoplates is more significant. It can be found that the flexural wavenumbers with surface effects are high as compared to that without surface effects. The scale effects show that the wavenumbers of the flexural wave become highly non-linear and tend to infinite at certain frequency. After that frequency the wave will not propagate and the corresponding wave velocities tend to zero at that frequency (escape frequency). The effects of surface stresses on the wave propagation properties of nanoplate are also captured in the present work.