| Summary: | 碩士 === 國立臺灣大學 === 機械工程學研究所 === 93 === 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 phononic crystal is studied in this thesis. Base on plane-stress assumption neglect the inertia effect of the displacement in the direction of thickness in dynamic situation. Modified plane-stress model is suitable for use in a wider frequency range.
First of all, the plane-stress and electric boundary conditions are employed to derive the strain and relative displacement because of Poisson effect, then we derive the governing equation by Hamilton principle. The plane wave expansion method and the Bloch theorem are used to modify the governing 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.
A study based on changing the materials, thickness, and electric boundary conditions is performed. We find that there is no difference between the dispersion curve of plane-stress model and modified plane-stress model in low frequency range. But the dispersion curve of modified plane-stress model will move down in high frequency range. Finally, by observing the phase of the displacement field, the dynamic situation of materials in the periodic structure is further understood that also provide useful information.
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