Single and Multiple Scattering of Inplane Waves by Nanofibers with Consideration of Interface Effects

Abstract

The single scattering by an individual nanofiber and the multiple scattering by unidirectionally arranged nanofibers embedded randomly in a host material for the propagation of incident plane P and SV waves perpendicularly to the axis of fibers are studied. By using the classical expansion method for wave functions, the incident, scattered, and refracted waves are expanded in series of cylindrical wave functions. The unknown expansion coefficients can be determined from interface conditions between the fiber and the host. The surface elasticity theory is used to consider the surface effects of nanofibers and to derive nontraditional interface conditions. The scattering cross section and the far-field scattering amplitude, which represent important information on the scattered wave, are discussed first. Then, the phase speed and the attenuation of the effective wave with multiple scattering effects are estimated based on the effective field approach and the configuration average. The influence of the interface effects of nanofibers on the scattering cross section, the far-field scattering amplitude and the effective propagation constants of elastic waves are discussed in detail on the basis of the numerical results obtained.