Effects of “Finiteness” on Wave Propagation and Vibration in Elastic Periodic Structures

Abstract

The dynamics of finite elastic periodically layered structures is compared to that of the constituent periodic media. The focus is on both the frequency behavior and the spatial response. Through simulations of harmonically induced wave motion within a finite number of unit cells, the frequency band structure and attenuation characteristics of infinite and finite periodic systems are shown to conform under certain conditions. It is concluded that only one or two unit cells of a periodic material are required for “frequency bandness” to carry through to a finite structure, and only three to four unit cells are necessary for significant wave attenuation to take place when the structure is excited at a stop-band frequency. Furthermore, vibration analyses are conducted on a bounded fully periodic structure. The natural frequency spread is shown to conform with the frequency band layout of the infinite periodic material, and the steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium. These results could be used for setting guidelines for the design of periodic structures for vibration isolation and frequency filtering.