Propagation of stress pulses in a Rayleigh-Love elastic rod

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.