); [EMAIL_ADDRESS] (J.Y. ); [EMAIL_ADDRESS] (Y.B. ); [EMAIL_ADDRESS] (Y.S. ); [EMAIL_ADDRESS] (T.H.) Yue Bao  
School of Transportation Science and Engineering, Beihang University, Beijing 102200, China; [EMAIL_ADDRESS] (H.L. ); [EMAIL_ADDRESS] (J.Y. ); [EMAIL_ADDRESS] (Y.B. ); [EMAIL_ADDRESS] (Y.S. ); [EMAIL_ADDRESS] (T.H.) Yue Bao  
School of Transportation Science and Engineering, Beihang University, Beijing 102200, China; [EMAIL_ADDRESS] (H.L. ); [EMAIL_ADDRESS] (J.Y. ); [EMAIL_ADDRESS] (Y.B. ); [EMAIL_ADDRESS] (Y.S. ); [EMAIL_ADDRESS] (T.H.) Yue Bao  
School of Transportation Science and Engineering, Beihang University, Beijing 102200, China; [EMAIL_ADDRESS] (H.L. ); [EMAIL_ADDRESS] (J.Y. ); [EMAIL_ADDRESS] (Y.B. ); [EMAIL_ADDRESS] (Y.S. ); [EMAIL_ADDRESS] (T.H.) Yue Bao  
School of Transportation Science and Engineering, Beihang University, Beijing 102200, China; liang605@buaa. in the plate greatly increases and the ABH effect remarkably weakens. Fortunately, the presence of a small amount of damping material on the surfaces of wedges with power-law profile can reduce the reflection coefficients significantly, despite the truncations [3; 4]. In addition, it has been demonstrated by using experimental investigation [5], and it also showed appealing potential in sound radiation control [6; 7]. A two-dimensional ABH is materialized by a cylindrically symmetrical indentation of power-law profile whose exponent is equal or larger than two. An important advantage of a two-dimensional ABH is that it can be embedded in a plate structure, which can widen the range of application. Many works on single two-dimensional ABHs have been done by using an analytical method. [PERSON] et al. [8] and [PERSON] [9] applied the geometrical acoustic theory to calculate the beam trajectories in the region of a two-dimensional ABH structure, and results showed that rays of waves propagated through the two-dimensional ABH region deflect to its central area. [PERSON] and [PERSON] et al. [10; 11] used the exact solution of the corresponding flexural wave equation to analyze the frequency response for circular and rectangular plates with and without ABH. They found that, despite the imperfect thickness profile, two-dimensional ABH structures with appropriate damping layers can also absorb a substantial amount of wave energy [9; 10; 11]. [PERSON] et al. [12] proposed a numerical integration scheme of the flexural ray equation to predict the ray trajectories of waves and investigated the wave focalization properties in two-dimensional ABHs. The plate embedded with a single two-dimensional ABH can address vibration absorption characteristics at higher frequencies where the plate bending wavelengths are smaller than the ABH characteristic dimension. However, for the vehicle body structure demanding better vibration and noise control performance at lower frequencies, the size of an ABH is limited by the size and shape of body panels. These limit the applicability of embedded ABHs as vibration and noise control solutions. Fortunately, a ABH array has the potential to improve the low-frequency vibration control performance of plate structure [5]. To understand the mechanisms of the flexural wave propagating in the ABH area, an analytical method can be used. However, it is difficult to analyze complex structures by this method such as a plate embedded with multiple two-dimensional ABHs. Numerical simulation based on the finite element method (FEM) can overcome the shortcoming of the analytical method and can be applied to both frequency domain analysis and time-domain analysis of ABH structures. [PERSON] et al. [13; 14] used the finite element and boundary element models to investigate the vibration and noise performance of plates embedded with periodic grids of embedded two-dimensional ABHs, and pointed out that the periodic ABH array may improve the low-frequency vibration control performance of the structure. Methods for enhancing low-frequency performance of the ABH effect were illustrated by [PERSON] et al. [6; 14].