Formation of bending-wave band structures in bicoupled beam-type phononic crystals

Beam-type phononic crystals as one kind of periodic material bear frequency bands for bending waves. For the first time, this paper presents formation mechanisms of the phase constant spectra in pass-bands of bending waves (coupled flexural and thickness-shear waves) in bicoupled beam-type phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closed-form dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberation-ray matrix (MRRM), based on which the bending-wave band structures in the bicoupled binary beam phononic crystal are found to be generated from the dispersion curves of the equivalent bending waves in the unit cell due to the zone folding effect, the cut-off characteristic of thickness-shear wave mode, and the wave interference phenomenon. The ratios of band-coefficient products, the characteristic times of the unit cell and the characteristic times of the constituent beams are revealed as the three kinds of essential parameters deciding the formation of bending-wave band structures. The MRRM, the closed-form dispersion relation, the formation mechanisms, and the essential parameters for the bending-wave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beam-type phononic crystals for wave filtering/guiding and vibration isolation/control.