Extremely low-frequency Lamb wave band gaps in a sandwich phononic crystal thin plate

Abstract

In this paper, a kind of sandwich phononic crystal (PC) plate with silicon rubber scatterers embedded in polymethyl methacrylate (PMMA) matrix is proposed to demonstrate its low-frequency Lamb wave band gap (BG) characteristics. The dispersion relationship and the displacement vector fields of the basic slab modes and the locally resonant modes are investigated to show the BG formation mechanism. The anti-symmetric Lamb wave BG is further studied due to its important function in reducing vibration. The analysis on the BG characteristics of the PC through changing their geometrical parameters is performed. By optimizing the structure, a sandwich PC plate with a thickness of only 3 mm and a lower boundary (as low as 23.9 Hz) of the first anti-symmetric BG is designed. Finally, sound insulation experiment on a sandwich PC plate with the thickness of only 2.5 mm is conducted, showing satisfactory noise reduction effect in the frequency range of the anti-symmetric Lamb BG. Therefore, this kind of sandwich PC plate has potential applications in controlling vibration and noise in low-frequency ranges.