The Study Of Band Structure Of Piezoelectric/Piezomagnetic Phononic Crystal

Phononic crystal is a kind of structures that the elastic parameters periodically arranged. Elastic or sound waves can be forbidden like photon propagate in photonic crystals and electron propagate in phonon glass-electron crystal when Elastic or sound waves propagate in phononic crystals, which is called band gaps. This unique character of dispersion of relation has many important potential application in the sound insulation, noise reduction, acoustic wave guide, acoustic lens, acoustic functional devices and metamaterial. Recently the research about phononic crystals made of functional materials such as piezoelectric materials and piezomagnetic materials become one of focuses in phononic crystals researches. These researches expect to use the piezoelectricity and piezomagnetism and initial stress to control the band gaps. While these researches consider electric field and magnetic field as quasi-static. In the thesis, we studied these phononic crystals considering the electric field and magnetic field to be dynamic and, consequently, piezoelectric composites are expected to have a dual role as a phononic crystal and a photonic crystal, as that of optomechanical crystals. The main researches and conclusion include:(1) Coupled elastic and electromagnetic waves propagating in piezoelectric materials and piezomagnetic materials are investigated considering the full system of Maxwell’s equations. The coupled wave equations derived. The interaction between displacement field and the electromagnetic field is analyzed, as the waves propagate in different directions. The results show that the propagation of elastic waves in some particular directions produce quasi-static electric field and magnetic field, but in some directions it will produce electromagnetic waves.(2) Using the coupled wave equations and the transfer matrix method and Bloch theory, we achieve the Closed-form expression of the dispersion relations of Coupled shear(SH) elastic and electromagnetic(EM) waves propagating oblique to a one dimensional periodic piezoelectric and piezomagnetic composite. The result shows that strong interaction between the elastic and EM waves near the center of the Brillouin zone(i.e., phonon-polariton) is revealed, and the piezoelectric and piezomagnetic effect can change the band structure of elastic branch.(3) The effect of biasing fields on the band gap of phononic crystals is investigated using the finite element method. The result shows that the initial shear stress can induce level repulsion and there isn’t level repulsion, when no initial shear stress is applied. The result is different with the result that the level repulsion can be found when there is no initial shear stress using plane wave expansion method. For highly symmetric inclusions wit the same filling rate, the band structures are almost the same.