Transient Torsional Waves in Stepped Circular Bars : Two-Dimensional Numerical Analysis and Its Experimental Verification

The present paper is concerned with a numerical and experimental investigation of the transient torsional waves in a semi-infinite stepped circular bar subjected to torsional impact loading at its free end. The differential equations governing the dynamic torsional deformation of the stepped bar are solved by means of the method of numerical integration along bi-characteristics. The stability and convergence of the numerical solutions are checked by estimating the total energy of the system. The torsional elastic wave-propagation experiments for the stepped bar are performed using a modified version of the torsional Hopkinson bar apparatus. The numerical results for the torsional shear strain-time profiles on the surface before and after the discontinuity of cross section of the stepped bar are shown to be in reasonable agreement with the experimental results. 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 discontinuity of the cross section of the stepped bar.