Based on constraint phononic crystal cutoff frequency characteristics, the paper studied effects on the phonon crystal band structure of the two-dimensional phononic crystal substrate density and elastic modulus under constraints. The spring quality equivalent model is proposed for the theoretical interpretation, and the results show that the equivalent model with similar constraints on phononic crystals bandgap structure has an important impact, and the cut-off frequency of phonon crystal is increased as the matrix density and elastic modulus increase. The further research of constraint phonon crystal band structure has important theoretical and practical significance for engineering of low-frequency vibration noise control.
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