Study on band gaps and defect bands in tunable phononic crystal plates with elastic foundations

Abstract

To analyze the band gap characteristics of phononic crystals, a two-dimensional phononic crystal plate model with an elastic foundation was first established. The plane wave expansion method was used to compute the dispersion curves of this phononic crystal model, and the results were compared with those from the finite element method to verify their accuracy. Subsequently, a parameter study explored the effects of the elastic foundation coefficient and coverage ratio on the band gap. The results indicate that as the coverage ratio of the elastic foundation increases, the band gap significantly expands, reaching its maximum value at 100% coverage. Additionally, as the elastic foundation stiffness increases, the band gap gradually widens and converges toward fixed boundary conditions. The study also investigated the band gap of phononic crystal plates with defects, finding that the vibrational energy concentrates at the defect unit cell. Furthermore, the defect band frequency can be effectively modulated by adjusting the coefficient of the elastic foundation, providing a theoretical basis for achieving efficient energy conversion.