Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity |
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Authors: | Zhi-Zhong Yan Chuanzeng Zhang |
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Institution: | a Department of Mathematics, Beijing Institute of Technology, Beijing 100081, PR China b Department of Civil Engineering, University of Siegen, D-57078 Siegen, Germany c Institute of Engineering Mechanics, School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China |
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Abstract: | The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence. |
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Keywords: | Aperiodic phononic crystal Disorder Localization factors Plane-wave-based transfer-matrix method Eigen-mode matching theory |
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