Theoretical and Experimental Investigation of Stress Waves at a Junction of Three Bars

When a longitudinal stress wave impinges on a junction of three elastic bars (where two bars are collinear and a third is noncollinear to the others), six separate stress waves are produced. A longitudinal stress wave and a flexural wave are reflected back along the first bar, and a stress wave of each type is transmitted into the second and third bars. For the theoretical treatment of these waves, the simple one-dimensional theory is used to describe the propagation of longitudinal (or axial) waves, and the Timoshenko beam theory is used to describe the propagation of transverse (or bending) waves. The method of characteristics is used to transform the partial differential equations into total differential equations. The total differential equations are then solved by a forward differencing finite-difference scheme. For solution at the junction, the junction is modeled as a rigid-body element. Impact experiments were performed to verify the analysis, and agreement between theory and experiment is very satisfactory.