Tunable bandgaps in novel two-dimensional piezoelectric phononic crystal slab

Abstract

One of the outstanding challenges in phononic crystal development is the ability to achieve bandgap tunability in a low frequency range. The introduction of piezoelectric materials into phononic crystals is an attractive technique for actively controlling the bandgaps, which is reliable, economical and light in weight. Phononic crystal possesses an artificial periodic composite structure whose elastic constant, density and sound velocity change periodically. When the elastic wave passes through a phononic crystal, special dispersion curve is formed due to the interaction among periodically arranged materials. In order to study the tunability of phononic crystal bandgap, we propose a novel two-dimensional piezoelectric phononic crystal structure possessing a wider complete bandgap, which is composed of piezoelectric materials with hard coatings periodically connected by four thin bars. The dispersion relation, transmission spectrum and displacement field are studied by using the finite element method in combination with the Bloch theorem. Numerical results show that the frequency of the first complete bandgap of the new designed phononic crystal slab is lower and the band width is enlarged by a factor of 5 compared with the band width of the traditional binary phononic crystal. Instead of changing the geometry or orientation of the phononic crystal units or inclusions, electrical boundary conditions are used to actively control the frequency bandgap. The boundary condition for electrical open circuit and short circuit are considered in this paper. With different electrical boundary conditions imposed on the surfaces of the piezoelectric inclusions, multiple complete bandgaps can be controlled actively, which means that the new designed phononic crystal structure can adapt to the vibration and noise reduction requirements under different vibration environments. The effect of piezoelectric effect on the band structure is investigated as well. The piezoelectric effect has a great influence on the band structure, with the increase of the piezoelectric constant, a part of bands move to high-frequency and the other part of the bands are kept at the original position, which means that the piezoelectric effect is of benefit to the opening of the complete bandgap. Furthermore, according to the tunability of the bandgap, the switchable piezoelectric phononic crystal slab waveguide is analyzed. Calculation shows that the electrical boundary defects can result in defect bands existing in the complete band gap, and the elastic wave energy flows can be limited by changing the applied electrical boundary conditions. This investigation is conducive to controlling the bandgaps and also reveals potential applications in designing the sensing system and different piezoelectric devices.