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We report on the theoretical analysis of locally resonant sonic band gaps (BGs) in a phononic crystal (PC) structure constituted by a square array of inclined cylindrical dots deposited on a thin homogeneous plate. Based on an efficient finite element method (FEM), we show that the PC plate with inclined dots can lower Lamb wave BGs due to a weak localized resonance of the edge of the upper surface of the inclined dots. The BGs can be effectively shifted by changing the value of the incline. The total displacement fields are computed to explain how the inclined dot induces the lowering of the locally resonant BGs. Transmission power spectra (TPS) are calculated to demonstrate the existence of the BGs and it matches well with the band structure. BGs evolution as a function of geometrical parameters of the PC plate with inclined dot is also studied. [ABSTRACT FROM AUTHOR]

In this paper, we theoretically investigate the propagation characteristics of Lamb waves in one-dimensional radial phononic crystal plates with periodic corrugations. The dispersion relations, the power transmission spectra, and the displacement fields of the eigenmodes are calculated by using the finite element method based on two-dimensional axial symmetry models in cylindrical coordinates. The axial symmetry model is validated by three-dimensional finite element model in rectangular coordinates. The effects of the geometrical parameters on the band gaps are further explored numerically. Numerical results show that several complete band gaps with a variable bandwidth exist for Lamb waves in the proposed structures. The formation mechanism of opening the acoustic band gaps is attributed to the coupling between the Lamb modes and the corrugation mode. The band gaps are significantly dependent upon the geometrical parameters such as the corrugation height, the corrugation width, and the plate thickness. Significantly, as the increase of corrugation height, band width shifts, new band gaps appear, the bands become flat, and the corrugation mode plays a more prominent role in the opening of Lamb wave band gaps. These properties of Lamb waves in the radial phononic crystal plates can potentially be applied to optimize band gaps, generate filters, and design acoustic devices. [ABSTRACT FROM AUTHOR]