【摘要】：經過二十多年的發(fā)展,一種存在彈性波帶隙特性、結構呈現(xiàn)周期性排列的復合聲學材料或結構,即聲子晶體,引起了越來越多的國內外學者的廣泛關注。這主要得益于聲子晶體擁有豐富的物理內涵以及廣闊的潛在應用前景。它的基本特征為:其一是存在聲子帶隙,這是其最顯著的物理特性,即聲子帶隙內頻率對應的彈性波/聲波傳播將受到抑制,在聲子晶體里會呈現(xiàn)指數(shù)衰減,而不能傳播,而其在通帶范圍內頻率對應的彈性波/聲波將可以實現(xiàn)無損耗地傳播;其二是具有缺陷態(tài)特性,當聲子晶體內部存在點缺陷、線缺陷或面缺陷時,則帶隙頻率范圍內的彈性波/聲波會被局域在點缺陷,或沿著線缺陷或面缺陷處傳播。這些特性使得聲子晶體可以設計成各式各樣的新型聲學器件,在機械振動、集成聲學及聲通信等領域有著廣闊的應用前景。聲子晶體作為一種新型人工周期性結構功能材料,已觀測并證實具有許多獨特的物理現(xiàn)象,如聲聚焦,自準直,負折射,Schoch效應。本文主要對聲子晶體Schoch效應展開研究,通過有限元方法,研究自準直聲波在二維三組元聲子晶體表面和聲學超表面上(以下簡稱超表面)的反射,實現(xiàn)了對聲子晶體的正向Schoch效應和超表面的負向Schoch效應的研究。本論文的內容安排如下:第一章首先介紹聲子晶體的概念及其基本特點,然后討論了聲子晶體國內外的研究現(xiàn)狀,最后敘述聲子晶體的幾個重要特性。第二章介紹了理想彈性介質條件中的彈性波波動方程,并利用散度和旋度算子分離出橫波和縱波。介紹二維聲子晶體三種常見的排列結構和聲子晶體帶隙的各種計算方法及其優(yōu)缺點,從彈性力學基本原理出發(fā)著重地介紹了有限元方法。第三章針對二維三組元聲子晶體Schoch效應進行了研究。本章設計了一種二維三組元聲子晶體-表面-水結構,通過有限元方法仿真了自準直聲波束在聲子晶體-表面層界面的反射情況,觀察到了聲子晶體表面的Schoch效應,并獲得反射波束產生Schoch位移與結構的關系。同時,利用模型超胞的能帶結構,分析了這一現(xiàn)象的原因,發(fā)現(xiàn)由于類波導模與體模的干涉作用,導致反射波束的非鏡面反射,即Schoch效應的產生是類波導模與體波模相互耦合的結果。另外,通過改變表面層包層的半徑,得到Schoch位移與包層的半徑的依賴關系。最后通過增加表面層層數(shù),調控兩層相同核圓柱的包層半徑,實現(xiàn)了對Schoch位移的增強,達到了對Schoch效應調控的目的。第四章主要研究聲波在超表面上反射的負向Schoch效應。通過在水中設計材料結構,實現(xiàn)水中負相位梯度超表面,進而研究超表面上聲波反射的負向Schoch效應。研究結果表明在設計的超表面上能夠明顯的觀測到聲波的負向Schoch效應。進一步我們研究了表面的厚度其對Schoch位移的影響。第五章闡述了本文的主要結論。
[Abstract]:With the development of more than 20 years, a kind of composite acoustic material or structure with elastic band gap and periodic structure, namely phonon crystal, has attracted more and more attention from scholars at home and abroad. This is mainly due to the rich physical connotations of phononic crystals and their wide potential applications. Its basic characteristics are as follows: one is the existence of phonon band gap, which is the most remarkable physical property, that is, the elastic wave / acoustic wave propagation corresponding to the frequency in phonon band gap will be restrained, and the propagation of elastic wave / acoustic wave in phonon crystal will be exponentially attenuated rather than propagated. The elastic wave / acoustic wave corresponding to the frequency in the passband range can propagate without loss. Secondly, it has the characteristic of defective state, when there is a point defect, line defect or plane defect in the phonon crystal, The elastic wave / acoustic wave in the band gap frequency range will be propagated locally at the point defect or along the line defect or the plane defect. These characteristics enable phononic crystals to be designed into a variety of novel acoustic devices, which have a broad application prospect in the fields of mechanical vibration, integrated acoustics and acoustic communication. As a new type of artificial periodic functional materials, phononic crystals have been observed and proved to have many unique physical phenomena, such as acoustic focusing, autocollimation, negative refraction and Schoch effect. In this paper, the Schoch effect of phonon crystals is studied, and the reflection of self-collimating sound waves on the surface of two-dimensional three-component phonon crystals and on acoustic supersurfaces (hereinafter referred to as supersurface) is studied by finite element method. The forward Schoch effect and the negative Schoch effect on the supersurface of the phonon crystal are studied. The contents of this thesis are as follows: in the first chapter, the concept and basic characteristics of phonon crystal are introduced, then the research status of phonon crystal at home and abroad is discussed, and several important characteristics of phonon crystal are described. In chapter 2, the wave equation of elastic wave in ideal elastic medium is introduced, and the S-wave and P-wave are separated by using divergence and curl operators. This paper introduces three kinds of common arrangement structure of two-dimensional phonon crystal, various calculation methods of band gap of phonon crystal and their advantages and disadvantages. The finite element method is emphatically introduced from the basic principle of elastic mechanics. In chapter 3, the Schoch effect of two-dimensional three-component phonon crystals is studied. In this chapter, a two-dimensional three-component phonon crystal surface-water structure is designed. The reflection of the self-collimated acoustic beam at the interface between the phonon crystal and the surface layer is simulated by finite element method, and the Schoch effect on the surface of the phonon crystal is observed. The relation between the Schoch displacement and the structure is obtained. At the same time, by using the energy band structure of the model supercell, the causes of this phenomenon are analyzed. It is found that the interference between waveguide mode and bulk mode leads to the non-mirror reflection of the reflected beam. That is to say, the generation of Schoch effect is the result of the coupling of wave-like mode and bulk mode. In addition, by changing the radius of the surface cladding, the dependence of the Schoch displacement on the cladding radius is obtained. Finally, by increasing the number of surface layers and adjusting the cladding radius of two layers of the same nuclear cylinder, the Schoch displacement is enhanced and the Schoch effect is adjusted. In chapter 4, the negative Schoch effect of acoustic wave reflected on supersurface is studied. By designing the material structure in water, the negative phase gradient supersurface is realized, and the negative Schoch effect of acoustic reflection on the supersurface is studied. The results show that the negative Schoch effect of acoustic waves can be observed obviously on the designed supersurface. Furthermore, the influence of the thickness of the surface on the Schoch displacement is studied. The fifth chapter describes the main conclusions of this paper.
【學位授予單位】：廣東工業(yè)大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O735

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相關期刊論文 前1條

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本文編號：2279993