Methodology for a Hopkinson test with a non-uniform viscoelastic bar

The conventional Hopkinson pressure bar method needs the use of uniform elastic bars with uniform mechanical characteristics and uniform cross-sectional area. In some particular cases, the impedance may be non-uniform in order to match the specimen impedance or if the bar is heated for high-temperature tests for instance. The method presented allows one to take the impedance variation of elastic or viscoelastic bars into account by using a transfer matrix. This transfer matrix can be predicted theoretically if the variations of the mechanical characteristics and of the cross-sectional area are known. If this is not the case, it is shown that the transfer matrix can be evaluated by a direct experimental method. This method is validated by tests performed on a viscoelastic bar having a significant impedance variation.