# Lamb波在抛物线型声黑洞薄板结构中的传播特性Study the Propagation Characteristics of Lamb Waves on Parabolic Acoustic Black Hole Thin Plate Structures

Abstract: In this paper, the propagation characteristics of Lamb waves on thin plate structure with parabolic acoustic black hole are studied by using laser ultrasonic technology. Based on the thermoelastic mechanism, a three-dimensional finite element model of laser excitation of Lamb wave in thin plate structure with parabolic acoustic black hole is established. Then, the acoustic wave propagates outward as the excitation region is the centre; the wave is parallel to the laser line source; and its propagation direction is perpendicular to the laser line source. When the sound wave encounters the acoustic black hole, it will propagate along the thickness decreasing direction. Meanwhile, the acoustic beam width decreases, and the amplitude gradually increases. Finally, the acoustic amplitude at the lowest point of the acoustic black hole increases gradually, which present the sound wave focusing phenomenon. The results of this paper can be used to detect and evaluate the thin plate structure with acoustic black hole.

1. 引言

Lamb波是平板按自由边界条件解波动方程时得到的一种特殊的波动解 [1]，被广泛应用于两个平行表面结构中的无损检测。利用其能量集中在薄板结构的上、下两个平面内，传播过程中衰减，可以实现非接触式激发，对于大规模薄板结构的无损检测具有极其重要的意义 [2]。

2. 理论研究

Figure 1. Schematic diagram of laser irradiation two-dimensional parabolic acoustic black hole structures

(a) 对称模态的Lamb波 (b) 反对称模态的Lamb波

Figure 2. Schematic diagram of symmetry and antisymmetry Lamb wave mode

$-k\frac{\partial T\left(x,y,z,t\right)}{\partial n}={I}_{0}A\left(T\right)f\left(x\right)g\left(t\right)$ (1)

$g\left(t\right)=\frac{8{t}^{3}}{{t}_{0}^{4}}\mathrm{exp}\left(\frac{-2{t}^{2}}{{t}_{0}^{2}}\right)$ (2)

$f\left(x\right)=\frac{1}{\sqrt{2\pi }}\frac{2}{{R}_{G}}\mathrm{exp}\left(\frac{-2{\left(x-{x}_{0}\right)}^{2}}{{R}_{G}^{2}}\right)$ (3)

Figure 3. The meshing of three-dimensional parabolic acoustic black hole structure

Table 1. Parameters of aluminum

3. 结果与讨论

(a) t = 0 μs (b) t = 0.5 μs(c) t = 1 μs (d) t = 1.5 μs

Figure 4. The displacement field of Lamb wave at 0 μs, 0.5 μs, 1 μs, 1.5 μs

(a) t = 2 μs (b) t = 3 μs(c) t = 4 μs (d) t = 5 μs

Figure 5. The displacement field of black hole at 2 μs, 3 μs, 4 μs, 5 μs

Figure 6. Schematic diagram of the center of black hole at (0 mm, 0 mm, 0 mm)

(a) (b)

Figure 7. (a) The displacement-time diagram and (b) the change of the peak displacement of the black hole center

4. 总结

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https://doi.org/10.1121/1.414211

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