Wave Propagation in Nanoscaled Periodic Layered Structures

In this paper the propagation of elastic waves in nanoscaled periodic layered structures is studied by using the nonlocal elastic continuum theory. The localization factor is introduced to describe the band structures for waves propagating either normally or obliquely in the system. Both the anti-plane and mixed in-plane wave modes are considered with detailed computations being performed for the nanoscaled HfO2-ZrO2 periodic layered structures. The localization factors as well as the dispersion curves are calculated to analyze the size-effect on the behaviors of the wave propagation. A cutoff 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. The generation and behavior of the band gaps with or without the mode conversion are also analyzed for the mixed in-plane wave modes.