Study on Lamb Waves in a Composite Phononic Crystal Plate

In the paper, a phononic crystal plate composed of a magnetorheological elastomer with adjustable band gaps in the low frequency range is constructed. The dispersion relations of Lamb waves are studied by the supercell plane wave expansion method. The transmission responses as well as the displacement fields of Lamb waves are calculated by the finite element method. The influence of geometric parameters on the band gaps, the regulation effect of the volume ratio of Fe particles and the bias magnetic field on the band gaps are analyzed. Based on the numerical results, we find that the volume ratio of Fe particles and the magnetic field affect the band gap effectively. The location and width of the band gaps can be adjusted within a broad frequency range by varying the geometric parameters and magnetic field. We can control the band gap, achieve an appropriate and wide low band gap by selecting proper geometric parameters and applying an external contactless magnetic field to deal with complicated and changeable engineering environment. The results are useful for understanding and optimizing the design of composite vibration isolation plates.