Shock jump equations for unsteady wave fronts

First, the Rankine–Hugoniot (R–H) relations are generalized for unsteady shock wave fronts of infinitesimal risetime. The equation for particle velocity has a term of strain rate, while that for stress contains terms of strain rate and acceleration. Next, shock jump equations of general form for particle velocity, stress, and specific internal energy are derived. They involve the combined effect of strain wave form, its change with time, and the path in time of strain. The effect, as well as the terms of strain rate and acceleration in the generalized R–H equations, indicates uncertainty about the applicability of familiar R–H equations to the shock fronts. Finally, jump equations for specific strain waves are evaluated: Jumps in the three quantities are influenced greatly by the effect. If both the wave form and the path are linear, then the equations are of the same form as the R–H equations.