Wave separation in non-uniform Hopkinson bars using redundant measurements

Abstract
In this paper we generalize the BCGO-wave separation method (Bussac, 2002, J. Phys. Mech. Solids, 50, 321-349) based on the maximum of likelihood principle to non-uniform rods. To achieve this aim, the force and the particle velocity at any cross-section are expressed as functions of the force and the particle velocity at the origin instead of the expressing them as function of the forward and downward waves. Due to this generalisation, one can perform long duration and medium strain-rate (1-100/s) tests using Hopkinson bars not only in the case of compression loadings but also for example dynamic bending and high-temperature tests. The new method is checked numerically on a stepped elastic bar. It shows good behaviour against noise.