Periodic Low Pitched Shudder Sound with Buick Century

Does anyone have ideas as to what may be going wrong with a 2002 Buick Century with about 80000 miles? Sometimes while braking there is a brief low pitched shuddering sound/vibration that lasts about 2 seconds. The tricky part is that sometimes the same event occurs when not braking. It seems to happen more often when braking however. My son thinks turning may be involved. He starts and stops harder than I and seems to experience the problem more than I. I am a gentle driver and am frustrated at not being able to recreate the problem but infrequently.

One brainstorming idea - The abs braking system?

Also check the front wheel bearings. Jack one front wheel off the ground; take a firm grip of the top and bottom of the tire and try to rock it/ wiggle it. Any movement the wheel bearing is bad. Repeat on other side.