In this paper, the longitudinal wave propagation in an elastic rod is studied based on the 1D Rayleigh-Love rod theory considering the lateral inertia effect. The Laplace transform method is applied to solve the initial boundary value problem. After conducting the inverse transform, a kernel function in form of integral is obtained, which reveals the essential dispersion characteristics of the wave propagation in a Rayleigh-Love rod. Then the general solution of stress is expressed as the convolution of the kernel function and the boundary loading. Specific examples are given for the problems of typical boundary pulses, i.e. the rectangular, trapezoidal, triangular, and two-stage pulses. Moreover, the dispersive waveforms from our analysis compare nicely with those from the finite element simulation, which indicates that our analytical solution can be used for the dispersion correction in the Hopkinson bar tests.

本文基于一维瑞利-洛夫杆理论，考虑了横向惯性效应，研究了弹性杆中的纵波传播问题。拉普拉斯变换方法用于解决初始边界值问题。进行逆变换后，获得了积分形式的核函数，该核函数揭示了波在瑞利-洛夫棒中传播的基本色散特性。然后将应力的一般解表示为核函数和边界载荷的卷积。给出了典型边界脉冲问题的具体示例，即矩形，梯形，三角形和两级脉冲。而且，我们分析的色散波形与有限元模拟的色散波形比较好，