Band Structure Calculations Of Elastic Waves Oblique Incidence To Two-dimensional Phononic Crystals By Multiple-scattering Theory

In rescent years, more and more works have been devoted to the study of the phononic crystals, especially for the band gaps. It is not only expected to make use of this artificial composite materials as sound insulator, sound filter, waveguide, and other acoustic elements materials, but also make us to better understand and reproduce some classical physical problems, such as the Anderson localization of elastic/acoustic waves, and so on. All of these physical problems and broad applications in phononic crystals are correlative to the phononic gap. Therefore, the investigation on the properties of phononic band gap is one of the interesting problems in the field of phononic crystals.In this thesis, after expanding the fields of displacement and stress with the scalar potential functions frequently used in the acoustics theory, we have extended the previous multiple-scattering theory through changing tensor operator into scalar operator, which is called the multiple-scattering theory of scalar potential function expansion. This method is not only simple and convenient, but also greatly reduces the difficulty of tensor operations.First of all, using the multiple-scattering theory of scalar potential function expansion, we have calculated the band structure of elastic waves normal and oblique incidence to two-dimensional solid/liquid phononic crystal, respectively. This method not only overcomes the convergence problem of the plane wave expansion method in solid/liquid systems, but also solves complicated mathematical operations resulting from the tensor operation used in the previous multiple-scattering theory method. From the calculated results, we have found that, with the increasing of the axial component of the incident wave vector, the band structure moves to high-frequency range as a whole. In low frequency range, a forbidden zone of the elastic waves propagating in two-dimensional periodic plane appears. Moreover, its width behaves wider with the increasing of the axial wave vector component.And then, the band structures of elastic waves normal and oblique incidence to two-dimensional solid/solid phononic crystals have been calculated. We have found that the band structures of the obliquely incidence are more complicated than those of the normal incidence. As the axial component of the oblique incident wave vector increasing, the band structure also moves to high-frequency range as a whole, and some new band gaps can be found, but the width of these new gaps is no longer behaving a simple law of increasing or decreasing with the axial wave vector component increasing. The propagation of elastic waves in the range of gaps is forbidden in the phononic crystals, so we can utilize the characteristics of these new gaps to insulate voice of different frequencies, or to localize elastic waves in the corresponding default structures. This research on the gap properties of oblique incidence has developed the applications of the phononic crystals.