From Longman Dictionary of Contemporary Englishput somebody under phrasal verbif a doctor puts you under, they give you drugs to make you unconscious before surgery → put→ See Verb table
Examples from the Corpus
put under• But don't be put off.• This, combined with the greater demands of the work, put them under a lot of pressure.• I rush out to put a barrel under at least one two-foot section of roof to catch some water.• She picked up her dog, put it under her arm, and walked briskly to her home.• He brought in a rug from New York Carpet World and put it under his desk.• The functions are now being put together under Sally Randall as trade publicity manager reporting to Eric Major.• He closed the case quickly and put it back under the seat.• Prison authorities put them under the wing of reputable agencies. 