摘要
Background, Motivation and Objective The propagation of surface acoustic waves(SAWs) in phononic crystals(PCs) has attracted a growing attention as they enable the realization of filtering, guiding and mirroring acoustic/elastic waves. Traditionally, the one-dimensional PCs consist of two alternating materials with a periodic spatial modulation of material density, elasticity, and piezoelectricity. Recently, D. Yudistira showed that the band gap of SAWs may be formed using one-dimensional periodic domain inversion through phonon-polariton coupling between the electromagnetic wave and acoustic phonons. Here we study Love waves in a novel PC which consists of periodic domain inversion piezoelectric substrate covered by a layer. The main motivation is to demonstrate the effects of layer on the band structure of Love waves. Statement of Contribution/Methods In this paper, finite element method is used to analyze the dispersive relation of the Love waves in phononic crystal structures. Compare with plane wave expansion method, finite element method is more simply and effective, only one-unit cell is needed for band structure calculations. The width of the unit cell is lattice constant a, and the thickness of the layer is h=0.2a. Theoretically the substrate is semi-infinite, fortunately, for surface wave that the height of the substrate is larger than several lattice periods can meet requirement. Based on Bloch theorem, Floquet periodic boundary condition is applied on the sides along the x-axis, the bottom of the unit cell is fixed and the surface of film is traction free. Results In order to demonstrate the existence of band gaps for Love waves in the structure, the proposed structures consisting of domain-inverted Barium titanate with an elastic layer is analyzed and discussed. The band gap appears at a frequency of about twice of the value expected from Bragg scattering. As we expected, the propagation of Love waves can be affected by the layer. The band structure can be easily tuned by changing the thickness of the layer. For instance, the frequency of the band gap decreases when the thickness increase. Discussion and Conclusions Love waves in a phononic crystal structure which consists of a periodic domain-inverted piezoelectric substrate covered by a homogeneous layer are studied. We calculate band gap of the Love waves using the finite element method. The band gap appears at a frequency of about twice of the value expected from Bragg scattering, formed through phonon-polariton. A series of calculations of band structures are performed to investigate the propagation of Love waves in different layer thickness. We show that the band structure is sensitive to the thickness of the layer.
Background, Motivation and Objective The propagation of surface acoustic waves(SAWs) in phononic crystals(PCs) has attracted a growing attention as they enable the realization of filtering, guiding and mirroring acoustic/elastic waves. Traditionally, the one-dimensional PCs consist of two alternating materials with a periodic spatial modulation of material density, elasticity, and piezoelectricity. Recently, D. Yudistira showed that the band gap of SAWs may be formed using one-dimensional periodic domain inversion through phonon-polariton coupling between the electromagnetic wave and acoustic phonons. Here we study Love waves in a novel PC which consists of periodic domain inversion piezoelectric substrate covered by a layer. The main motivation is to demonstrate the effects of layer on the band structure of Love waves. Statement of Contribution/Methods In this paper, finite element method is used to analyze the dispersive relation of the Love waves in phononic crystal structures. Compare with plane wave expansion method, finite element method is more simply and effective, only one-unit cell is needed for band structure calculations. The width of the unit cell is lattice constant a, and the thickness of the layer is h=0.2a. Theoretically the substrate is semi-infinite, fortunately, for surface wave that the height of the substrate is larger than several lattice periods can meet requirement. Based on Bloch theorem, Floquet periodic boundary condition is applied on the sides along the x-axis, the bottom of the unit cell is fixed and the surface of film is traction free. Results In order to demonstrate the existence of band gaps for Love waves in the structure, the proposed structures consisting of domain-inverted Barium titanate with an elastic layer is analyzed and discussed. The band gap appears at a frequency of about twice of the value expected from Bragg scattering. As we expected, the propagation of Love waves can be affected by the layer. The band structure can be easily tuned by changing the thickness of the layer. For instance, the frequency of the band gap decreases when the thickness increase. Discussion and Conclusions Love waves in a phononic crystal structure which consists of a periodic domain-inverted piezoelectric substrate covered by a homogeneous layer are studied. We calculate band gap of the Love waves using the finite element method. The band gap appears at a frequency of about twice of the value expected from Bragg scattering, formed through phonon-polariton. A series of calculations of band structures are performed to investigate the propagation of Love waves in different layer thickness. We show that the band structure is sensitive to the thickness of the layer.
引文
