How can I access information about the effect of friction dampers (Coulomb dry friction) on the dynamic equation of motion? Also the effects of this type of damping on the energy balance equation.
the dynamic energy balance equation is certainly affected due to introduction of friction damper(s) based on Coulomb's dry friction. Even if the friction damper(s) would be based on some other friction mechanism/ type, e.g., wet friction (with Stribeck effect) the dynamic equilibrium equations are changed, so does the energy balance equation as well. Some of these effects (albeit not all) have been studied and reported in the following article:
Chapter Energy Assessment of Friction Damped Two Dimensional Frame S...
Hope you would find detailed answers to your questions from the equations given the abovementioned article for evaluating and ascertaining energy balance. Still, if you have further questions please feel free to ask.