Eigenmode matching theory, which was developed originally for the band structure and the transmission property of the infinite phononic crystal ( PC), is extended to deal with the PC thin plate. By this method, the transmission property of the one-dimensional PC thin plate with and without a uniform substrate is investigated. It is shown that in the PC thin plate without a substrate, the permitted band of the structure can be separated into two parts, which can be excited by the incident antisymmetric and symmetric Lamb modes, respectively. However, for the PC plate with a substrate, the energy conversion between the symmetric and antisymmetric modes can be found in the transmission spectrum. The physical origin of such an energy conversion is discussed.
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