A numerical and experimental study of transient torsional waves in stepped circular bars

A numerical and experimental investigation into the reflection and transmission of transient torsional waves at a discontinuity of cross-section in stepped circular bars is presented. The differential equations governing the torsional motion of the stepped bar are solved by application of the method of bicharacteristics. The stability and convergence of the numerical solutions are checked by estimating the total energy in the system. The torsional elastic wave-propagation experiments for a stepped steel bar are carried out using a modified torsional Hopkinson bar. The numerical solutions for the torsional shear strain histories at several positions before and after the discontinuity of cross-section in the stepped steel bar are shown to be in reasonable agreement with the experimental data. The limitations of the classical one-dimensional torsional wave equation for thin rods are examined by determining the two-dimensional distributions of the dynamic torsional shear stresses in the vicinity of the cross-sectional discontinuity in the stepped bars. The advantages and limitations associated with the method of bicharacteristics are discussed.