Wave Propagation in Nanoscaled Periodic Layered Structures

Abstract

In this paper the elastic waves propagating normally and obliquely in the nanoscaled quasi-periodic layered structures are studied by using the nonlocal elastic (NLE) continuum theory. The NLE theory includes the effects of the long range interatomic forces by supposing that the stress-state at a point is related to the strain-state at all points of the entire body. The conception of the localization factors are introduced to describe the band structures for waves propagating either normally or obliquely in the nanoscaled system. Both the anti-plane and mixed in-plane wave modes are considered. The localization factors as well as the dispersion curves and the transmission spectra are calculated to analyze the behaviors of the wave propagation. A cut-off frequency is found, beyond which waves cannot propagate through the system. The influences of the ratio of the internal to external characteristic lengths on the cut-off frequency and band structures are discussed.