应力波在杆形部件中的传播与反演设计

应用矩阵方法，研究了应力波在弹性杆形部件中的传输特性。推导了以顺波、逆波为状态向量的应力波传播方程和杆形部件的作用力、速度传播的特征矩阵；探讨了特征矩阵及各元素的表达形式和特性；定义了部件透射率和反射率。基于给定部件的特征矩阵，采用多项式根的替换方法，反演递推求解出给定部件等透射率的部件设计方案；从设计方案的多项式根的分布状态和部件外部形态等方面探讨了设计方案数与离散单元数的关系。

Propagation and Inverse Design of Stress Wave in an Elastic Bar

By applying a matrix approach, the stress wave propagating in an elastic bar is studied. Stress wave propagation equations that incident wave and reflection wave are condition vectors are derived from three discrete forms as well as the characteristic matrix of the force and the velocity. The expressions and properties of the characteristic matrix and its elements are discussed. The transmissibility and reflectivity of parts are defined. Based on the characteristic matrix of a given part, all parts with the same transmissibility as the given part can be obtained inversely through substitution of polynomial roots. The relation between the number of designed parts and that of the divided segments are discussed with respect to the distribution of polynomial roots on a complex plane and the changes of the shape of the parts.