集中质量边界条件下声子晶体杆的纵向振动传递特性研究

Transmission characteristics of longitudinal vibration of a phononic crystal rod with concentrated mass boundary condition

为分析集中质量边界下声子晶体杆的纵向振动传递特性,建立了树脂杆、铝杆及"树脂+铝"声子晶体杆模型,计算了0～50 kHz范围内自由边界和集中质量边界两类情况下三种杆的振动传递率,并进一步分析了集中质量大小对传递率的影响。分析结果表明:自由边界下树脂杆和铝杆均无减振性能,而声子晶体杆则呈现出3个明显的带隙;集中质量边界下树脂杆和铝杆能够在较宽的频带内抑制振动的传递,但其传递率曲线存在很多共振峰,不利于减振,而声子晶体杆的带隙在此边界下仍能显著抑制振动的传递,从而明显改善了减振性能,但集中质量可能引入强烈的共振峰;随着集中质量的增加,三种杆的减振性能进一步提高。

In order to obtain transmission characteristics of longitudinal vibration of a phononic crystal rod with concentrated mass boundary condition, models of an epoxy rod, an aluminum one and an ＂epoxy ＋ aluminum＂ pnononic crystal one were built and the transmissibility curves of longitudinal vibration of these rods were calculated between 0 50KHz with free boundary condition and concentrated mass boundary condition, respectively. Furthermore, the influences of different concentrated masses on the transmissibility were analyzed. The analysis results showed that with free boundary condition, both the expoxy rod and the aluminum one have no ability of vibration reduction, while three obvious stop bands can be found for the phononic crystal rod ; with concentrated mass boundary condition, vibration can be reduced in a wider frequency band for both the epoxy rod and the aluminum one while many resonance peaks can be found in their transmissibility curves, they are harmful to vibration reduction, vibration can be suppressed apparently with the effect of stop bands for the phononic crystal rod and therefore its vibration reduction ability is improved much more; nevertheless, sharp resonance peaks may be induced by concentrated mass, they impair these rods＇ ability of vibration reduction distinctly; with increase in concentrated mass, the vibration reduction ability of three types of rods can be enhanced.