Research on the elastic wave band gaps of curved beam of phononic crystals

Based on wave equations of Timoshenko curved beam, the theoretical derivation and numerical calculation of the behavior of in-plane and out-of-plane wave propagating in curved beam of phononic crystals (CBPC) are carried out using transfer matrix method combined with the Bloch theorem. Finite CBPC is also simulated by FEM method. It is shown that both in-plane and out-of-plane elastic waves band gaps exist in CBPC. Compared with equivalent straight beam of phononic crystals (SBPC), CBPC has some unique characteristics, such as the first complete in-plane band gap, special in-plane coupling band gap, and out-of-plane coupling band gap. In those band gaps, CBPC has a better property of vibration reduction than the equivalent SBPC in some ways. Furthermore, effects of curvature of CBPC on the in-plane and out-of-plane band gaps are discussed.