梯度密度黏弹性材料的波传播研究

梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征，基于控制方程的Euler形式，利用Laplace变换，得到了这种材料中的波传播规律的一个理论公式；并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛（Ti-TiB₂）材料和碳纤维树脂材料，采用不同的叠合方向和方式，利用分离式霍普金森压杆（split Hopkinson pressure bar，SHPB）加载装置进行了动态冲击实验，并用三波法对得到的实验结果进行处理。同时，采用数值Laplace逆变换方法，结合SHPB测得的入射波与透射波数据，使用推导的理论公式计算出理论解，并与实验结果进行了比较。结果表明:（1）梯度钛-硼化钛材料由于内界面和叠层界面的存在，表现出一定的黏性特性；单层Ti-TiB₂材料的计算结果和三波法分析得到的结果基本一致，双层Ti-TiB₂材料叠合后的计算结果与三波法分析结果存在一定的差异。（2）双层碳纤维树脂材料表现出较强的黏弹性特征，应力波的衰减幅度较大，三波法分析结果与该材料的冲击性能有较大的差异。由此可知，无论是细微观结构特征产生的黏性，还是材料本身的黏性，对材料动力学行为的影响都不可忽略。。

Wave propagation in density-graded viscoelastic material

Wave propagation in visco-elastic materials with gradient density is really complex. In order to understand the responses of the visco-elastic materials to impact load, a series of theoretical equations for wave propagation in density-graded visco-elastic materials were proposed by employing the Euler form of the governing equations and the Laplace transform method. According to these equations, the wave propagation in the two-layer periodically-superimposed media with perpendicular incidence was analyzed. The Ti-TiB₂ material with gradient density characteristics and the carbon-fiber-reinforced resin composites with strong visco-elastic properties were selected as experimental subjects to carry out dynamic impact tests by applying a split Hopkinson pressure bar (SHPB) device. To better reflect the influences of the gradient characteristics on the dynamic responses of the materials, the experimental specimens were prepared by using different stacking directions and modes. The data obtained by the SHPB device were analyzed by the three-wave method. Moreover, according to the incident wave and transmission wave obtained by the SHPB device, the wave propagation equations proposed for the visco-elastic media with gradient density were applied to obtain the corresponding theoretical solutions. And the calculated theoretical solutions were compared with the experimental results. The comparisons display as follows. (1) Due to the internal interface and the superimposed interface, the graded Ti-TiB₂ materials show certain viscosity properties. For single-layer Ti-TiB₂ specimens, the theoretically calculated results are approximately consistent with the experimental ones analyzed by the three-wave method. But there lie some differences for two-layer Ti-TiB₂ specimens. (2) The two-layer carbon fiber reinforced resin composites exhibit stronger visco-elastic characteristics, and the attenuation amplitude of stress wave is larger. There are obvious differences between the experimental results analyzed by the three-wave method and theoretically calculated ones. As a consequence, the influences of the viscosity produced by the meso-structures and the viscosity of the material itself on the dynamic behaviors of the macro medium cannot be ignored.