Lamb waves in double-layered nanoplates

摘要

This paper is concerned with the propagation of Lamb waves in double-layered nanoplates and a nonlocal continuum model is presented. Each layer of the double-layered nanoplates is coupled through the van der Waals interaction. The equations of wave motion are derived and dispersion relations are obtained. The present model predicts some notable features of the dispersion relations in double-layered nanoplates, in comparison with Lamb waves in classic plates in vacuo. By considering the van der Waals interaction, some modes appear in pairs at the same frequency, their phase velocities are very close at a given frequency. Some modes only propagate in a very narrow frequency band and may disappear above certain frequencies. The small-scale has significant influence on the propagation characteristics of Lamb waves. Larger values of the scale coefficient result in lower escape frequencies and phase velocities of Lamb waves.