Phononic plate waves

In the past two decades, phononic crystals (PCs) which consist of periodically arranged media have attracted a lot of interests due to the existence of complete frequency band gaps and maneuverable band structures. Recently, Lamb waves in thin plates with PC structures started to receive increasing attention for their potential applications in filters, resonators, and waveguides. This paper presents a review of recent works conducted by the authors and co-workers on this topic. Both theoretical and experimental studies of Lamb waves in two-dimensional (2D) PC plate structures are covered. On the theoretical side, analyses of Lamb waves in 2D phononic plates using the plane wave expansion (PWE) method, finite-difference time-domain (FDTD) method, and finite-element (FE) method are briefly addressed. These methods were applied to determine the frequency ranges of the complete band gaps of Lamb waves, characteristics of the propagating and localized eigenmodes that can exist in the PC plate structures, and behavior of anomalous refraction called negative refraction. The theoretical analyses demonstrated the effects of PC based negative refraction, lens, waveguides, and resonant cavities. We also discuss the influences of geometrical parameters on the guiding and resonance efficiency and the frequencies of waveguide and cavity modes. On the experimental side, we present design and fabrication of a silicon based Lamb wave resonator which utilizes PC plates as reflective gratings to form the resonant cavity of Lamb waves. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs are applied.