battery light flickers and car shudders lightly on 2012 Elantra-Not the Battery

Has anyone had this problem: During the first 10 or 15 minutes that my car is
on, the battery light flickers and when the light flickers on and off, my car kind
of convulses lightly. Last night this happened, and I noticed that the headlights
and interior light go up and down in this rhythm. It's almost like I am revving
the car. This particularly happens if I put it in D or R and just sit there with the
brake on.
Had my battery replaced today. No change.