Journal
PHYSICA B-CONDENSED MATTER
Volume 407, Issue 23, Pages 4579-4583Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physb.2012.08.022
Keywords
Phononic crystal; Euler beam; Modified transfer matrix method; Band structure
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Funding
- National Natural Science Foundation of China [50808066, 50978085]
- Research and Innovation Project for College Graduates of Jiangsu Province
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We introduce a modified transfer matrix (MTM) method for the calculation of the bending vibration band structure of one-dimensional phononic crystal (PC) Euler beams. A particular combination of hyperbolic functions and triangular functions is introduced to transform the state parameters of the transfer matrix (TM) method into four initial parameters, which have the explicit meanings of the displacement, rotation angle, bending moment and shear force at one beam end. The method is used to calculate the band structures of two PC Euler beams constructed from aluminum-Lucite and 100 kinds of materials respectively. The effectiveness and high efficiency of the MTM method are demonstrated by the results. Several advantages make it a proper choice for the calculation of the bending vibration band structure of PC Euler beams. (C) 2012 Elsevier B.V. All rights reserved.
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