A319 Captain reported during takeoff a shuddering of the entire aircraft resulted in a rejected takeoff.

Narrative

When cleared for takeoff from ZZZ Runway XXC; immediately there was a very pronounced shuddering of the entire aircraft. I said reject my aircraft at approximately 30 knots. I then stopped the aircraft and set the parking brake followed by the PA announcement ' this is the captain; remain seated; remain seated; remain seated'. When we attempted to clear the runway the ZZZ ATC Tower reported that with aircraft movement smoke appeared to come from the left main landing gear area. We stopped with no further incident. ZZZ Airport Rescue and Firefighting arrived and reported no smoke or fire. The temperatures of the landing gear were all normal. They remained nearby. I then contacted Dispatch and Maintenance Control and the decision was made to deplane the passengers and have maintenance take control of the aircraft. I informed the passengers of the plan to deplane and return to the terminal followed by several PA's to assure them that the situation was under control and there was no danger. The passengers seemed to be in good spirits when deplaning with many thanking us for keeping them safe. Mechanical failure.