One-dimensional linear elastic waves at moving property interface

Smart materials exhibit time-varying properties while time-varying external field is applied. To investigate the one-dimensional (1-D) homogeneous time-varying properties, a moving property interface (MPI) model is proposed, and the propagation of linear elastic waves at 1-D MPI is studied in this paper. Based on the idea of weak solutions and an infinity approximation, a novel method to deal with the difficulties in using the continuities to study the waves at MPI is also proposed. Some interesting phenomena are revealed: (i) besides wave impedance, the property interface motion and wave velocity are also very important factors that influence the wave propagation; (ii) at MPI, there may exist shock waves; (iii) the property interface motion has a significant impact on the wave frequency and energy. This research provides a theoretical viewpoint in the study of smart materials with a time-dependent mechanical properties at different loading conditions.