The Frequency Spectrum of Piezoelectric Periodical Laminated Plates with the Plane Wave Method Analyses
Date Issued
2006
Date
2006
Author(s)
Liu, Kuo-Chung
DOI
zh-TW
Abstract
The dissertation focuses on the phenomenon of wave propagation of piezoelectric periodical composite laminated plate. By using the motion equations and Gauss theorem cooperative with constitutive relations of piezoelectricity, the governing equations can be determined. Because the governing equations have the relationship of translation symmetry, the displacement fields and the electrical potential fields can be represented by Bloch theorem to get the periodical structural governing equations.
For gaining the band structure of piezoelectric periodical composite laminated plate, the boundary conditions of the upper and lower surfaces should be satisfied first, where the boundary conditions can be determined with the transfer matrix from the coefficients between layers and layers, such as displacements, stresses, electrical potentials, and electrical displacements, on condition of continuity. These coefficients result from the formal expressions of displacement fields and electrical potential fields, according to the constitutive relations of piezoelectricity.
To verify the derived results from above mathematical analyses, the experiment is applied. The experiment is set up with these two instruments, laser Doppler vibrometers and spectrum analyzer, to observe the response of the electric discharge pulse strikes. The observation is for the band relations from the reactions of two periodical structures, the aluminum alloy cylinders in a PMMA background and the air cylinders in a PMMA background. Compared these observed results with the band gaps of these dispersion curves from the plane stress in the plane wave method, our mathematical analyses provided good agreement.
Moreover, the mathematical analyses can be applied to more or even infinite layers structures. The probing for piezoelectric effects to transverse polarization on a two-dimensional structure of the infinite thick plate is designed, where the wave-vector component parallel to the structure is zero. The band structure is calculated for this piezoelectric periodical structure. The relationship of band gaps and filling fraction is therefore obtained. A discussion on isotropic periodical structures without the assumption of the wave-vector component parallel to the structure being zero is provided. We rule out these structures with the band gaps also. According to this rule, the formulations for isotropic periodical plates with different thickness are generated. The formula for three-layer structures can be determined from formulas of single-layer structures. Besides, the frequency spectrum diagram can be plotted according to the formula. In the frequency spectrum diagram, there are only local band gaps found.
Subjects
壓電週期結構
疊層板
平面波法
頻帶間隙
頻譜
piezoelectric periodical structure
laminated plate
plane wave method
band gap
frequency spectrum
Type
thesis
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