Propagation of Surface and Lamb Waves in Two-Dimensional Piezoelectric Phononic Crystals
Date Issued
2007
Date
2007
Author(s)
Hsu, Jin-Chen
DOI
en-US
Abstract
ABSTRACT
Phononic crystals are composite materials which consist of homogeneous elastic inclusions distributed periodically in a background medium characterized by different physical properties, such as mass density and elastic stiffness. Thus far, numbers of released researches have demonstrated the possible usage of phononic crystals for acoustic manipulations, such as acoustic mirrors/refractive devices, high-efficiency waveguides with frequency modulation in the transmittivity, tunable filters, and de-multiplexers, etc, based on the localization and the formation of frequency band gap of acoustic waves in such periodic composites. For high-frequency applications and academic interests, phononic crystals comprised of piezoelectric materials and the propagation of guided waves like the surface modes and plate modes in such composites are important to study.
In this study, the propagation of bulk acoustic waves, surface acoustic waves, and Lamb/plate waves in phononic-crystal structures containing piezoelectric constituents is theoretically investigated. First, the basis in the description of periodic structures is briefly introduced. Next, the full three-dimensional plane wave expansion (PWE) method is utilized to develop the mathematical formulation by integrating the method into the governing field equations of waves in piezoelectric solids. Then the nume- rical calculations are presented to analyze the dispersion relations or the frequency band structures of acoustic waves and to discuss the effects of lattice symmetries, filling fractions of inclusions, material contrasts, and piezoelectricity on the complete frequency band gaps.
In particular, the characteristics of surface modes and plate modes in phononic- crystal structures are probed. The periodicity of the structure results in a dispersive property for the electromechanical coupling coefficients of surface waves and the existence of pseudosurface waves. In addition, the Bleustein-Gulyaev surface wave, which has no counterpart in a non-piezoelectric medium, in ZnO/CdS piezoelectric phononic crystal and the folding effect are found. Moreover, propagation of Lamb waves in plate structure created by a phononic crystal is analyzed by introducing boundary conditions for another plane surface into the PWE formulation. In addition to the lattice symmetries, filling fractions, and material contrasts, the existence and the width of complete band gaps of Lamb waves are crucially affected by the ratio of the plate thickness to the lattice period.
Finally, Mindlin’s plate theory is applied to address the problem of lower order Lamb modes in a phononic-crystal plate. Compared to the full three-dimensional PWE method, Mindlin’s theory based PWE formulation has excellent performance in coping with the phononic-crystal plate consisting of constituents with large acoustic mismatch and/or inclusions with a non-smooth contour in their cross section such as square rods that need to sum over numerous plane waves to ensure the convergence by reducing the computation time considerably. The frequency band structures of locally resonant phononic-crystal plates and subfrequency band gaps are calculated as well.
In brief, the PWE methods to analyze the propagation of bulk waves and guided waves in two-dimensional piezoelectric phononic-crystal structures are formulated, and their characteristics are investigated and discussed in this work.
Subjects
聲子晶體
晶格
表面聲波
板波
壓電晶體
平面波展開法
局部共振
Phononic Crystal
Lattice, Surface Acoustic Wave
Lamb Wave
Plane Wave Expansion Method
Piezoelectric Crystal
Local Resonance
Type
thesis
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