Study of wave propagation in nanowires with surface effects by using a high-order continuum theory

Abstract

A high-order continuum model is developed to study wave propagation in nanowires. By using the model, heterogeneous nanostructure effects can be captured especially for high wave frequency cases. Surface stress effects are also included by using the incremental deformation approach. The governing equations of motion in the nanowire are derived including both the strain-independent and strain-dependent surface stresses. For simplicity and clarity, specific attention will be paid to the effects of strain-independent surface stress in this study. The accuracy of the proposed model is validated by comparing dispersion curves of longitudinal wave propagation from the current model with those from the exact solution. By conducting a reduced formulation, the results predicted by the current model will be compared with those based on existed high-order models to show capability of the current model. Numerical simulations are then conducted to study both longitudinal and flexural wave propagation in nanowires. The surface stress effects upon both longitudinal and flexural wave propagation in nanowires are demonstrated, from which the size dependent wave information in nanowires can be observed. Some new physical wave phenomena related to the surface stress effects are discussed.