Lamb waves in phononic band gap structures

Phononic crystals (PCs) which consist of periodically arranged media have, in the past two decades, attracted intensive studies due to their renewed properties of 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 twodimensional (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 addressed. These methods were applied to determine the frequency ranges of band gaps of Lamb waves and characteristics of the propagating and localized eigenmodes that can exist in the PC plate structures. The theoretical analyses demonstrated the effects of PC based waveguides and resonant cavities. We 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 discuss band gaps of Lamb waves in a surface stubbed phononic plate made of aluminum which were demonstrated using laser ultrasonics. Furthermore, we present design and fabrication of a silicon based two-port Lamb wave resonator which utilizes PC reflective gratings to form the cavity. The measured results showed significant improvement of the insertion losses and quality factors of the resonators when the PCs were applied.