Transient waves in a rod subjected to impulsive end loading

Abstract

SUMMARYHerein the propagation of transient waves in a rod due to impulsive end loading is investigated using the method of wavefront expansion. The Mindlin-Herrmann equations which include the Poisson effect are used to model the rod. Since this rod theory is restricted to lower values of Poisson's ratio ( < 0.283), the present work also has the same restriction. The impulsive end loading on the rod can be prescribed in the form of stress, strain, velocity or acceleration boundary conditions. The analysis is based on the concept of a wave as a camer of discontinuities in the field variables and their derivatives. These discontinuities are determined from a set of recurrence relations which are in turn generated by the use of time harmonic asymptotic series solutions to the equations of motion. Transients due to both velocity and strain (or stress) boundary conditions are treated. Numerical examples are presented to illustrate the method of solution. The results indicate the distortion of the transient waves due to the dispersive nature of the governing equations. Transients due to other boundary conditions at the rod end can be treated by using the results presented in the paper.