Impact of Input Signal Characteristics on Energy-Localization Performance of a Phononic Crystal with a Defect: A Comparative Study of Burst and Continuous Wave Excitation

Abstract

This study examines the energy-localization performance of a one-dimensional phononic crystal (PnC) with a defect when exposed to burst waves of different cycle numbers under longitudinal waves. Using the finite element method, band structures of the defect-introduced PnC were calculated, revealing a phononic band-gap range, defect-band frequencies, and corresponding defect-mode shapes. The transient analysis examined the longitudinal displacement at the center of this defect in the time domain for various burst-wave scenarios. The results indicate that energy-localization performance inside the defect highly depended on the number of cycles. Energy-localization performance was better with larger cycles or continuous waves, although burst waves with a small number of cycles also showed some improvement, albeit limited. Moreover, burst waves with a small number of cycles did not clearly induce fixed-like boundary conditions (in other words, nodal points in standing waves) within the defect-introduced PnC, leading to obscure energy-localized behaviors. Key messages from this work can be summarized as follows. First, comparing the energy-localization performance under incident burst waves with different cycle numbers for different systems might not be appropriate. Second, the physically reasonable formation of defect-mode-enabled energy localization requires burst waves with a large (in the case study, over 500) number of cycles.