In this paper, localization phenomena of in-plane time-harmonic elastic waves propagating in layered phononic crystals (PNCs) with different fractal superlattices are studied. For this purpose, oblique wave propagation in layered structures is considered. To describe wave localization phenomena, the localization factor is applied and computed by the transfer matrix method. Three typical fractal superlattices are considered, namely, the Cantorlike fractal superlattice (CLFSL), the golden-section fractal superlattice (GSFSL), and the Fibonacci fractal superlattice (FFSL). Numerical results for the localization factors of CLFSL, GSFSL, and FFSL are presented and analyzed. The results show that the localization factor of a CLFSL exhibits an approximate similarity and band-splitting properties. The number of decomposed bandgaps of the GSFSL and FFSL follows the composition of the special fractal structures. In addition, with increasing fractal series, the value of the localization factor is enlarged. These results are of great importance for structure design of fractal PNCs.
Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 31, 2012; final manuscript received October 19, 2012; published online June 6, 2013. Assoc. Editor: Mahmoud Hussein.
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Yan, Z., Zhang, C., and Wang, Y. (June 6, 2013). "Elastic Wave Localization in Layered Phononic Crystals With Fractal Superlattices." ASME. J. Vib. Acoust. August 2013; 135(4): 041004. https://doi.org/10.1115/1.4023818
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