Band Gaps Study for Two-Dimensional Piezoelectric Phononic Crystals
Date Issued
2004
Date
2004
Author(s)
Chi, Chou-Chi
DOI
zh-TW
Abstract
Possessing the properties of band gaps, phononic crystals have led the invention of many new devices. In order to handle this characteristic potential, the spectrum of a plane-stress piezoelectric photonic crystal is studied in this thesis. First of all the plane-stress and electric boundary conditions are employed to derive the equivalent elastic moduli. The plane wave expansion method and the Bloch theorem are used to modify the wave equation into the one fit for periodic structures. The material parameters and displacement fields are expanded with Fourier series with respect to reciprocal lattice vectors. Finally, a generalized eigenvalue problem is formed that is solved with numerical method to obtain the frequency spectrum and the displacement fields. The band gaps are found from the frequency spectrum.
In order to handle the frequency span of band gaps, a study based on changing the materials, the filling ratio and the shape of inclusions is performed. Wide band gaps can be achieved by using composite inclusions that is made of two different kinds of materials. When metals are used as the core materials that are surrounded with PMMA to form the inclusions, and piezoelectric material as the host matrix provides very wide band gaps. In addition, the effects of electrodes are also studied. Finally, by observing the phase of the displacement field, the locus of particles in the periodic structure is further understood that also provide useful information.
Subjects
平面應力
聲子晶體
頻帶間隙
三種材料
壓電
平面波展開法
phononic crystal
piezoelectric
band gap
three component
plane-stress
plane wave expansion method
Type
thesis
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