Abstract
In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.
Highlights
Phononic crystal[1] is a kind of functional periodic structures
In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves
The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges
Summary
Phononic crystal[1] is a kind of functional periodic structures. It can be either composites periodically composed of two or more components, or systems with periodic patterns. The unique property of the phononic crystal is the possibility to exhibit a bandgap in the considered wave propagation direction, within which the propagation of elastic/acoustic waves is completely prohibited This phenomenon is of interest for practical applications such as wave filters and vibrationless environment for high-precision mechanical systems or other acoustic devices.[2]. We study the band structures and directional wave propagation in beam-like zigzag lattice structures with bending arms[13,14] by using the finite element method. Both the in-plane and out-of-plane propagating waves are taken into account simultaneously via the threedimensional Euler beam elements. The phase constant surface of one typical mode and the propagation of time-harmonic elastic waves in the finite structure with point sources at different locations are computed to show the directional properties of the systems
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