Over the past two decades, propagation of acoustic waves in periodic structures comprised of multi-components has received much attention because of renewed physical properties and potential applications in a variety of fields, such as noise and vibration isolation, frequency filters in wireless communication, super lens design, etc. These composite materials, called phononic crystals (PCs) [1,2], give rise to forbidden gaps for acoustic waves which are analogous to the band gaps for electromagnetic waves in photonic crystals. Major mechanisms leading to the forbidden gaps are Bragg scattering and localized resonances (LR) [3]. The former opens up the Bragg gap at the Brillouin-zone boundaries, and the band-gap frequency corresponds to the wavelength in the order of the structural period, i.e. of the lattice constant, and relates to the lattice symmetry. On the other hand, localized