Surface effect on size-dependent wave propagation in nanoplates via nonlocal elasticity

Abstract

Within the framework of nonlocal elasticity, the surface layer model is proposed to investigate the wave propagation characteristics in a single-layered nanoplate. The general solutions of nonlocal governing equations are expressed using partial wave technique and the nonclassical boundary conditions are derived. The dispersion relation with the effects of surface and nonlocal small-scale is obtained, and the size-dependent dispersion behaviour is demonstrated. The impacts of surface elasticity, residual surface stress and nonlocal parameter on the dispersion curves of the lowest-order two modes are illustrated. Numerical examples reveal that both the surface effect and nonlocal small-scale effect can obviously decrease the magnitude of phase velocity, and the thinner nanoplate corresponds to the smaller wave velocity and the narrower frequency bandwidth.

Keywords:

• surface effect
• nonlocal elasticity
• wave propagation
• nanoplate
• dispersion relation

Acknowledgement

The first author also would like to acknowledge the support provided by the Fundamental Research Funds for the Central Universities (No. C12JB00170).