"The purpose of the PhD. qualifying examination is to determine whether the student has the intellectual maturity, readiness and ability to begin engaging in doctoral research."
Most students take the qualifying exams or "quals" in their second or third semester. They must select 3 mechanical engineering disciplines in which they will be examined by a panel of professors.
Students choose from:
Solid Mechanics
Controls
Vibrations
Design
Thermodynamics
Fluid Mechanics
Heat Transfer
A description of the qualifying exam and each discpline can be found here.