Surface effects on frequency dispersion characteristics of Lamb waves in a nanoplate

Dispersion of Lamb waves in a nanoplate where surface effects exist is investigated in this work by combining the wave theory with the surface elasticity theory. The frequency dispersion equations of the symmetric and the anti-symmetric modes are derived and numerically solved. It is found that surface effects give rise to the thickness-dependent frequency dispersion, and that the phase velocity of Lamb waves increases with the decrease of the plate thickness. Two surface elastic constants featuring surface effects in terms of the surface elasticity theory exhibit significant influence on the wave frequency dispersion in the nanoplate. The larger the surface elastic constants, the higher the wave phase velocity. Moreover, the impact of surface effects is more prominent for the symmetric Lamb waves within the low frequency range. In particular, the symmetric Lamb wave velocity of the fundamental mode can be correlated to the surface elastic constants and the plate thickness when the wave frequency tends to zero. Finally, based on the frequency dispersion characteristics of the symmetric Lamb waves, an analytical expression is given to determine the surface elastic constants according to the wave phase velocity.