Abstract
Existing band gap analysis is mostly focused on the binary structure, while the researches on the quaternary layered periodic structure are still lacking. In this paper, the unidimensional lumped-mass method in the phonic crystal theory is firstly improved so that the material viscoelasticity can be taken into consideration. Then, the binary layered periodic structure is converted into a quaternary one and band gaps appear at low frequency range. Finally, the effects of density, elastic modulus, damping ratio, and the thickness of single material on the first band gap of the quaternary layered periodic structure are analyzed after the algorithm is promoted. The research findings show that effects of density, elastic modulus, and thickness of materials on the first band gap are considerable but those of damping ratio are not so distinct. This research provides theoretical bases for band gap design of the quaternary layered periodic structure.
Highlights
In recent years, the researches on energy band features of periodic structure constructed artificially based on the phononic crystal theory have drawn more and more attention
Afterwards, the researchers [4,5,6] studied the influence of material properties on phononic band gaps and found that the main reason why phononic band gaps occurred lied in periodic variation of material properties like the density and elastic modulus
The quaternary layered periodic structure is first simplified into a unidimensional phononic crystal structure according to the phononic crystal theory, and the effects of density, elastic modulus, damping ratio, and thickness proportion of each type of material on the first band gap are analyzed with the lumped-mass method
Summary
The researches on energy band features of periodic structure constructed artificially based on the phononic crystal theory have drawn more and more attention. Hussein et al [8, 9] studied the layered periodic structure constructed with two types of materials and obtained the band gap features in the variation of material distribution in each period They observed the vibration of the corresponding finite periodic structure and the results showed that the damping features could be fully embodied when the number of periods reached a certain value. The quaternary layered periodic structure is first simplified into a unidimensional phononic crystal structure according to the phononic crystal theory, and the effects of density, elastic modulus, damping ratio, and thickness proportion of each type of material on the first band gap are analyzed with the lumped-mass method
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