Wave propagation in a semi-infinite heteromodular elastic bar subjected to a harmonic loading

In this paper we deal with one-dimensional wave propagation in a material that reacts differently to compression and tension. A possible approach to describe such materials is the heteromodular (or bimodular) elastic theory: a piece-wise linear theory with different elastic moduli depending on the stress state. We consider a one-dimensional problem concerning non-stationary wave propagation in a semi-infinite heteromodular elastic body subjected to a suddenly applied harmonic loading. For a medium where the difference of elastic moduli for tension and compression is a small quantity, we obtain an approximate analytical solution of the problem using an asymptotic technique. Then we compare the asymptotic solutions obtained with numerical results and demonstrate a good agreement between them. The spectral characteristics of the constructed solution can be compared with experimental data obtained from dynamical experiments with materials displaying pronounced heteromodular properties.