Dispersion curves, mode shapes, stresses and energies of SH and Lamb waves in layered elastic nanoplates with surface/interface effect

Abstract

In this paper, we derive the formulations and carry out the calculation on the wave motion characteristics in layered nanostructures based on the surface/interface elasticity (effect). While the general solution in each bulk layer is obtained in terms of the mathematically elegant and numerically powerful Stroh formalism, the surface/interface constitutive relation is converted into a matrix form which is similar to the bulk layer matrix for easy propagation. To derive a stable global matrix for the layered structures, the dual variable and position method is utilized. Furthermore, the dispersion curves are calculated by a recently presented accurate algorithm. Numerical results show that the surface/interface effect can be significant when the wavenumber is large and the thickness of the layer is small. Besides its effect on the dispersion curves and mode shapes, the nanoscale surface/interface could further change the kinetic and strain energy on the wave. Particularly, a reduction in surface energy, which corresponds to a negative surface energy, could cause the nanostructure unstable.