基于半解析法的一维圆锥形声学黑洞梁能量聚集效应研究

Analysis of the Energy Concentration Effect of Flexural Vibrations in Tapered Rods with Power-law Profile based on Semi-analytical Method

声学黑洞(Acoustic Black Hole,ABH)效应是弯曲波在楔形结构中传播时波速逐渐减小至零从而不发生反射的现象。由于弯曲波在理想黑洞结构中不发生反射,这就意味着能量被集中在楔形结构的尖端部分,这一现象使得黑洞结构在减振降噪,能量回收等领域中具有极大的应用潜力。为了对截面呈幂率变化的杆结构进行动力学分析,首先建立相应的物理模型,然后利用小波函数拟合杆振动时的挠度曲线并结合拉格朗日方程建立系统的动力学方程;通过对其进行求解得到系统的振动响应。分析计算结果可知,相较于均匀杆结构,截面呈幂律变化的杆结构能够有效的抑制其振动;进一步比较楔形梁和圆杆的振动响应表明,黑洞结构对两者振动响应的抑制效果相似,但锥形杆的尖端聚能效果要优于楔形梁结构。

The acoustic black hole（ABH） effect is the phenomenon that the wave velocity decreases gradually to zero without reflection when the bending wave propagates in wedge-shaped structure, and the energy is completely concentrated on the tip of the wedge structure. This phenomenon makes this sort of structure to have a great potential of application in the fields of vibration reduction and energy recovery. In this paper, the physical model was established for dynamics analysis of a tapered rod structure with ABH. The wavelet function was adapted to fit the deflection curve of the rod. Furthermore, the dynamic equation of the system was established based on the Lagrange equation. Then, the vibration response was obtained by solving the dynamic equation. The results of analysis and calculation show that compared with the uniform rod structure,this rod structure with ABH can effectively suppress the vibration. Further comparison of the vibration response of the wedged beam and the tapered rod shows that both of them own similar effect on vibration reduction, but the energy accumulation effect of the tapered rod is better than that of the wedged beam.