Large bandgaps of two-dimensional phononic crystals with cross-like holes

Abstract

In this paper we study the bandgap properties of two-dimensional phononic crystals with cross-like holes using the finite element method. The influence of the geometry parameters of the holes on the bandgaps is discussed. In contrast to a system of square holes, which does not exhibits bandgaps if the symmetry of the holes is the same as that of the lattice, systems of cross-like holes show large bandgaps at lower frequencies. The bandgaps are significantly dependent upon the geometry (including the size, shape, and rotation) of the cross-like holes. The vibration modes of the bandgap edges are computed and analyzed in order to clarify the mechanism of the generation of the lowest bandgap. It is found that the generation of the lowest bangdap is a result of the local resonance of the periodically arranged lumps connected with narrow connectors. Spring-mass models are developed in order to predict the frequencies of the lower bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

Formation of Bragg Band Gaps in Anisotropic Phononic Crystals Analyzed With the Empty Lattice Model

“…The phononic band structure can be computed numerically using several methods such as multiple scattering theory [3,4], plane wave expansion [5][6][7], and finite element method [8][9][10]. However, it is also important to understand how the band structure forms and how it is affected by the geometry of the phononic crystal and properties of constituent materials.…”

Coupling local resonance with Bragg band gaps in single-phase mechanical metamaterials

“…A more practical and promising solution are single-phase metamaterials, which have attracted increasing interest in the community [29][30][31][32][33][34][35][36][37][38], and in which both types of BGs have been shown to be present [39][40][41][42][43]. However, to the best of our knowledge, the conditions and physical mechanism of the coupling of Bragg BG with local resonances in single-phase structures has not yet been analyzed.…”

Reducing symmetry in topology optimization of two-dimensional porous phononic crystals

“…The optimized structures can be modeled as mass-spring systems, i.e., the solid lumps act as masses and the bars as the springs. 59 It is seen from the modes O 1 , O 3 and O 5 that the lumps vibrate strongly and the bars vibrate slightly for the lower-edge modes. However, for the upper-edge modes O 2 , O 4 and O 6 , the situation is the reverse.…”