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Interaction and Multiscale Mechanics   Volume 6, Number 1, March 2013, pages 15-29
DOI: https://doi.org/10.12989/imm.2013.6.1.015
 
Theoretical analysis of transient wave propagation in the band gap of phononic system
Yi-Hsien Lin and Chien-Ching Ma

 
Abstract     [Buy Article]
    Phononic system composed of periodical elastic structures exhibit band gap phenomenon, and all elastic wave cannot propagate within the band gap. In this article, we consider one-dimensional binary materials which are periodically arranged as a 20-layered medium instead of infinite layered system for phononic system. The layered medium with finite dimension is subjected to a uniformly distributed sinusoidal loading at the upper surface, and the bottom surface is assumed to be traction free. The transient wave propagation in the 20-layered medium is analyzed by Laplace transform technique. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin\'s formula) is performed to obtain the transient response in time domain. The numerical results show that when a sinusoidal loading with a specific frequency within band gap is applied, stress response will be significantly decayed if the receiver is away from the source. However, when a sinusoidal force with frequency is out of band gap, the attenuation of the stress response is not obvious as that in the band gap.
 
Key Words
    phononic system; band gap; multilayered; transient wave; laplace transform; durbin
 
Address
Yi-Hsien Lin and Chien-Ching Ma: Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
 

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