Theoretical And Experimental Research On The One-dimensional Phonon Band Gap Structure Of The Ideal And "defective.

The phononic crystals, which derived from the natural crystals in solid state physics as the photonic crystals, are composite of different materials arranged periodically. The component materials have different destiny and elastic parameter. Because of the periodic arrangement of the atomic potential field, the electronic state in the solid was showed as band structure. With the same periodicity, the phononic crystals have the similar feature, only the energy band structure is derived to the macro sense of the elastic wave. In1995, R. Martinez-Sala et.al confirmed the presence of the elastic band gaps experimentally. Then, more in-depth research, more interesting phenomena and laws about the phononic crystals have been revealed. These important properties of the phononic crystals showed a broad application prospects in noise damping, acoustic waveguide, sound filtering and other aspects.In this field, most attention was focused on the study of the band structure characteristics of the phononic crystals. the formation process of elastic wave band structure has not been study basically. In recent years, the study of the phononic crystals with structure defects is also attracted by many scholars, such as cycle defects, lattice mismatch, inter-layers. These studies have shown that the phononic crystals with structure defects will appear some similar natures to the electrons in the solid crystals, such as Bloch oscillations, Zener resonant tunneling effect. And some specific defects will cause the change of the transmission characteristics of the elastic wave in phononic crystals. Most of these quantitative calculations haven’t study the evolution of phonon band structure characteristics with the defects change.Based on this, this article is mainly consisted by the following works:(1) According to the basic theory of the electronic state of nature crystals in modern solid state physics, we have investigated the discontinuity of the energy spectrum of the finite phononic crystals. And adapt the Lump-Mass method to calculate the band structure of different cycle one-dimension finite phononic crystals, discussed the evolution of the elastic wave transmission characteristics with the increase of cycles of the crystal. The results show that the energy spectrum of ideal finite phononic crystal is also discrete. As to N cycles phononic crystal, within the passband, there are N discrete transmission wave frequency, and with the increase of the number of cycles, the band structure is gradually formed.And we have designed experiment to verify the conclusion above. In the experiment we have modulated the original signal to get broadband motivate acoustic to research the transmission properties of waves in the band frequency, this work laid an important experimental basis for the subsequent works. The phononic crystals used in the experiment in which the theoretical results were verified were3,5,7cycles. In a certain degree, the study has some guiding significance to the actual application of the phononic crystals.(2) This article also has investigated the band structure of phononic crystals which with inter-layer in the lattice. This content is composed by two aspects:on the one hand, based on Lump-Mass method to study the band structure of phononic crystals which has been modulated by the inter-layer (that is, the "defect") with different material parameters. On the other hand, based on the Transfer Matrix theory study the acoustic wave transmission regularity of the resonant system, when the inter-layer is the same material, but having different thicknesses. The theoretical results show that the inter-layer will introduce a new transmission frequency into the band structure of the original phononic crystal. The process is similar to the Zener resonant tunneling effect in quantum mechanics.In the experiment, by constituting an adjustable acoustic resonator with two identical phononic crystals, change the length of the resonator cavity; study the dynamic tunneling evolution at the edge of the band gap. The experiment confirmed theoretical analysis results, and revealed the dynamic evolution of acoustic transmission spectrum in the system change with the material parameters and the thickness of the cavity.