Phononic crystals (PnCs) are a class of materials that are capable of manipulating elastodynamic waves. Much of the research on PnCs, both theoretical and experimental, focus on studying the transmission spectrum of PnCs in an effort to characterize and engineer their phononic band gaps. Although most studies have shown acceptable agreement between the theoretical and experimental bandgaps, perfect matches are elusive. A framework is presented wherein two and three dimensional harmonic finite element analyses are utilized to study their mechanical behavior for the purpose of more accurately predicting the spectral properties of PnCs. Discussions on a Harmonic Finite Elements Analysis formulation of a perfectly matched layer absorbing boundary and how reflections from absorbing boundaries can be inferred via standing wave ratios are provided. Comparisons between 2D and 3D analyses are presented that show the less computationally intensive 2D models are equally accurate under certain conditions. Finally, it is shown that a surface excitation boundary condition in a 3D model can significantly improve understanding of the experimental results for PnCs excited by surface mounted excitation sources.

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