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Abstract: The band structures of flexural waves in a phononic crystal thin plate with straight, bending or branching linear defects are theoretically investigated using the supercell technique based on the improved plane wave expansion method. We show the existence of an absolute band gap of the perfect phononic crystal and linear defect modes inside the gap caused by localization of flexural waves at or near the defects. The displacement distributions show that flexural waves can transmit well along the straight linear defect created by removing one row of cylinders from the perfect phononic crystals for almost all the frequencies falling in the band gap, which indicates that this structure can act as a high efficiency waveguide. However, for bending or branching linear defects, there exist both guided and localized modes, and therefore the phononic crystals could be served as waveguides or filters.

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