Characteristic Of 2D Phononic Crystalwith Archimedean Lattices

Phononic crystal (PC) is a kind of the new functional material which shows the rich phenomena. It is the striking interesting for many potential applications such as vibration attenuation, control sound, transducers, acoustic lters, super lens, acoustic cloaking and so on.The effect of lattice configuration can play an important role to manipulate propagation of elastic waves or acoustic waves in periodic media. Generally, lattice configurations of 2D PCs are mainly the familiar Bravais lattices, but the ancient 2D Archimedean lattices have been attracted a lot of attention. There are 11 2D Archimedean lattices that are periodic structures and the higher order of local symmetries as quasicrystals. Therefore, 2D PCs with Archimedean lattices may have many unique characters in promising potential applications. In this thesis, the band gaps, defect states and sound isolation of 2D phononic crystals with Archimedean lattices have been investigated by the theoretical and experimental methods as follows:(1) Based on the general wave equation proposed by Léon Brillouin, the governing equations of TE waves, TM waves, elastic shear waves and acoustic pressure waves in the fabricated periodic media can express a universal wave equation. So we have the developed the universal plane wave expansion method to calculated band structures of man-made crystals. In accordance with the universal wave equation, it can explain the ordinary meaning of physics for classical wave phenomena.(2) We can obtain the rigid periodicity of PCs with Archimedean lattice fabricated by laser processing technology. Moreover, based on the well-known ultrasonic immersion transmission technique, an experimental setup is designed to measure the band gaps and defect states of 2D PCs.(3) The ranges of frequency of band gaps for 2D steel-water PCs with the square and honeycomb lattices are investigated experimentally and theoretically. Then, band gaps stability for finite-sized 2D steel-water PCs with square lattice has been investigated experimentally. A single defect, defect mode waveguide and waveguide of line for 2D steel-water PC with square lattice have been measured experimentally.(4) The existence of complete band gaps is first verified experimentally and theoretically for 2D steel-water PC with ladybug and bathroom lattices. Then, band gap stability and isotropy for finite-sized 2D steel-water PCs with ladybug lattice is analyzed. A single defect, defect-mode waveguide and waveguide of wave shape for 2D steel-water PCs with ladybug lattice have been measured experimentally. The results show that the defect-mode waveguide and waveguide of wave shape can form the good pass band. Finally, band structures of solid-solid and liquid-liquid systems for 2D PCs with square-like Archimedean lattices are calculated by plane wave expansion method. The isotropy of band gap and relation of band gap to mid-gap ratio and normalized radius are analyzed.(5) The feature of band gaps is first demonstrated experimentally and theoretically for 2D steel-water PC with (3.4.6.4) lattice, so the result show the many narrow complete band gaps can appear duo to Archimedean lattice with higher order of local symmetries. Finally, based on the plane wave expansion method, band structures of solid-solid and liquid-liquid systems for 2D PCs with triangular-like Archimedean lattices are calculated. The isotropy of band gap and relation of band gap to mid-gap ratio and normalized radius are analyzed. Furthermore, the relation of band gap to mid-gap ratio and normalized radius of above two systems for 2D PCs with (3.4.6.4) and (34.6) lattices in lower frequency region are discussed.(6) The properties of 2D stainless steel tubes-air phononic crystals with (3.4.6.4), (34.6), ladybug, bathroom, honeycomb, triangular and square lattices have been investigated theoretically by plane wave expansion method. Then, the designed tandem structures with Archimedean and Bravais lattices are regarded as noise barriers and can reduce the harm of human body within the human audible range of frequencies.