Based on the nonlocal elastic continuum theory, the band structures of the nano-sized layered phononic crystals are analyzed by computing the localization factors and dispersion curves. Detailed calculations are performed for a nanosized HfO2–ZrO2 periodic layer stack. The size-effect on the band structures is examined. It is found that the nonlocal elastic continuum solution deviates from the classical elastic continuum theory and finally approaches the first-principle result as the thickness of each individual layer decreases. Due to the size-effect, there exists a cut-off frequency beyond which the waves cannot propagate through the system.
Analysis of Band Structures of Nanosized Phononic Crystals by Nonlocal Elastic Theory
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Wang, Y, & Chen, A. "Analysis of Band Structures of Nanosized Phononic Crystals by Nonlocal Elastic Theory." Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition. Volume 9: Micro- and Nano-Systems Engineering and Packaging, Parts A and B. Houston, Texas, USA. November 9–15, 2012. pp. 605-609. ASME. https://doi.org/10.1115/IMECE2012-86701
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