The dynamic response of component bolted joints often plays a significant role in the overall behavior of a structural system. Accurate finite element simulation of these problems requires proper treatment of the interface conditions. We present a formulation carefully suited to these problems that incorporates discontinuous Galerkin (DG) treatment locally at the interface. The present work is an extension of our previous investigations of friction models within a finite element method for quasi-static problems. The current emphasis is on the treatment of the inertial term and ensuring that artificial resonance is not induced by the discrete interface. The weak imposition of continuity constraints allows the stick-slip behavior at the jointed surface to proceed smoothly, reducing the numerical instability compared to node-to-node contact techniques. As a model problem, we simulate the dynamic response of a lap joint subjected to an impulse axial force assuming Coulomb friction at the interface.