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Crystals 2018, 8(1), 21;

Analysis of Bending Waves in Phononic Crystal Beams with Defects

School of Civil Engineering and Mechanics, Lanzhou University, and Key Laboratory of Mechanics on Disaster and Environment in Western China, Ministry of Education, Lanzhou 730000, China
Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, School of Aeronautics and Astronautics, Institute of Applied Mechanics, Zhejiang University, Hangzhou 310027, China
Author to whom correspondence should be addressed.
Received: 15 October 2017 / Revised: 21 December 2017 / Accepted: 3 January 2018 / Published: 6 January 2018
(This article belongs to the Special Issue Phononics)
PDF [4959 KB, uploaded 6 January 2018]


Existing investigations on imperfect phononic crystal beams mainly concern periodic multi-span beams carrying either one or two channel waves with random or deterministic disorder in span-length. This paper studies the two channel bending waves in phononic crystal beams consisting of many phases of materials with defects introduced as one structural segment having different cross-sectional dimensions or material parameters. The method of reverberation-ray matrix (MRRM) based on the Timoshenko beam theory, which can conduct high-frequency analysis, is extended for the theoretical analysis of dispersion and transmission of bending waves. The supercell technique and the Floquet–Bloch theorem are adopted for modeling the dispersion characteristics, and the whole finite structural model is used to calculate the transmission spectra. Experimental measurements and numerical calculations are provided to validate the displacement transmission obtained by the proposed MRRM, with the effect of damping on transmission spectra being concerned. The high-frequency calculation applicability of the proposed MRRM is also confirmed by comparing the present results with the corresponding ones either using the transfer matrix method (TMM) or MRRM based on Euler—Bernoulli beam theory. The influences of defect size, defect form, and unit-cell number on the transmission spectra and the band structures are discussed. The drawn conclusions may be useful for designing or evaluating the defected phononic crystal beams in bending wave control. In addition, our conclusions are especially potential for identifying the defect location through bending wave signals. View Full-Text
Keywords: phononic crystals; periodic beams; defects; disorders; method of reverberation-ray matrix; band structures; transmission spectra phononic crystals; periodic beams; defects; disorders; method of reverberation-ray matrix; band structures; transmission spectra

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Guo, Y.; Li, L.; Chuang, K.-C. Analysis of Bending Waves in Phononic Crystal Beams with Defects. Crystals 2018, 8, 21.

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