One-Dimensional Phononic Crystals. In: Deymier PA, editor. Acoustic Metamaterials and Phononic Crystals. Berlin: Springer Berlin Heidelberg; 2013. pp. 45-93. [DOI: 10.1007/978-3-642-31232-8_3]

Quality Factor Enhancement of Piezoelectric MEMS Resonator Using a Small Cross-Section Connection Phononic Crystal

Anchor loss is usually the most significant energy loss factor in Micro-Electro-Mechanical Systems (MEMS) resonators, which seriously hinders the application of MEMS resonators in wireless communication. This paper proposes a cross-section connection phononic crystal (SCC-PnC), which can be used for MEMS resonators of various overtone modes. First, using the finite element method to study the frequency characteristics and delay line of the SCC-PnC band, the SCC-PnC has an ultra-wide bandgap of 56.6-269.6 MHz. Next, the effects of the height h and the position h₁ of the structural parameters of the small cross-connected plate on the band gap are studied, and it is found that h is more sensitive to the width of the band gap. Further, the SCC-PnC was implanted into the piezoelectric MEMS resonator, and the admittance and insertion loss curves were obtained. The results show that when the arrangement of 4 × 7 SCC-PnC plates is adopted, the anchor quality factors of the third-order overtone, fifth-order overtone, and seventh-order overtone MEMS resonators are increased by 1656 times, 2027 times, and 16 times, respectively.

Stoneley-type waves in anisotropic periodic superlattices

The paper investigates the existence of interfacial (Stoneley-type) acoustic waves localised at the internal boundary between two semi-infinite superlattices which are adjoined with each other to form one-dimensional phononic bicrystal. Each superlattice is a periodic sequence of perfectly bonded homogeneous and/or functionally graded layers of general anisotropy. Given any asymmetric arrangement of unit cells (periods) of superlattices, it is found that the maximum number of interfacial waves, which can emerge at a fixed tangential wavenumber for the frequency varying within a stopband, is three for the lowest stopband and six for any upper stopband. Moreover, we show that this number of three or six waves in the lowest or upper stopband, is actually the maximum for the number of waves occurring per stopband in a given bicrystal plus their number in the "complementary" bicrystal, which is obtained by swapping upper and lower superlattices of the initial one (so that both bicrystals have the same band structure). An example is provided demonstrating attainability of this upper bound, i.e. the existence of six interfacial waves in a stopband. The results obtained under no assumptions regarding the material anisotropy are also specified to the case of monoclinic symmetry leading to acoustic mode decoupling.

Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell

The paper is concerned with the interfacial acoustic waves localized at the internal boundary of two different perfectly bonded semi-infinite one-dimensional phononic crystals represented by periodically layered or functionally graded elastic structures. The unit cell is assumed symmetric relative to its midplane, whereas the constituent materials may be of arbitrary anisotropy. The issue of the maximum possible number of interfacial waves per full stop band of a phononic bicrystal is investigated. It is proved that, given a fixed tangential wavenumber, the lowest stop band admits at most one interfacial wave, while an upper stop band admits up to three interfacial waves. The results obtained for the case of generally anisotropic bicrystals are specialized for the case of a symmetric sagittal plane.