Rosberg has been on the podium in his last two races.
Team principal Ross Brawn told the autosport.com website that Mercedes has been puzzled by the difference in performance and had decided to strip down Hamilton's car to conduct a detailed analysis.
"We had a very good look at the car and we found that the chassis was quite badly damaged - more than we thought," he said.
"We knew he had had some excursions over kerbs and things, but when we actually got here and started to strip everything down, the damage was pretty significant. It may even be at a level that was affecting the handling of the car."
Hamilton told reporters in Austin that his form since the end of the August summer break had been 'shocking' and wondered if it was something to do with the direction taken in setting up the car.
He has said after Abu Dhabi, where he suffered a rear wishbone failure as he ran over a kerb in the final qualifying session, that the car felt like it had an extra 50kg on board.
"In the last race the qualifying didn't help and it spiralled down from then on," he said.
"I am hoping this weekend to put myself in a better position."
(Writing by Alan Baldwin in London; Editing by John O'Brien)
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