Formation of Bending Wave Band Structures in Bicoupled Beam Type Phononic Crystals

Abstract

Beamtype 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 passbands of bending waves (coupled flexural and thicknessshear waves) in bicoupled beamtype phononic crystals based on the model of periodic binary beam with rigidly connected joints. Closedform dispersion relation of bending waves in the bicoupled periodic binary beam is obtained by our proposed method of reverberationray matrix (MRRM), based on which the bendingwave 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 cutoff characteristic of thicknessshear wave mode, and the wave interference phenomenon. The ratios of bandcoefficient 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 bendingwave band structures. The MRRM, the closedform dispersion relation, the formation mechanisms, and the essential parameters for the bendingwave band structures in bicoupled binary beam phononic crystals are validated by numerical examples, all of which will promote the applications of beamtype phononic crystals for wave filtering/guiding and vibration isolation/control.