Abstract: Based on the vibrational equation of the one- dimensional thin rod phononic crystals composed of two kind of material, the vibrational wave and surface wave implicit dispersion relation in periodically layered infinite and semi- infinite media are provided. The width of band gaps and surface wave frequency both relate with the material portion ratio. For the phononic crystals with a free surface, the necessary condition for the existence of the surface localized modes in the free surface is found to be the velocity of the material with free surface less than that of the other material. Using the finite element method, the vibrational frequency response of finite- size phononic crystals and found the particular resonance peak due to the surface localized modes in the band gaps is calculated. These resonance peaks decreae the frequency response attenua- tion at least 20 dB.

Key words: Phononic crystals, Surface localized modes, Vibration band gap