According to the pilot of the Cessna 172N, while completing touch and go landings, the airplane bounced on the first landing. She took off again and completed another "loop" in the pattern. The pilot returned to land at the airport a second time, which was "very smooth." She taxied the airplane back to the hangar, shut down the engine, exited the airplane, and saw the propeller was bent a "small amount." The pilot was unaware of the propeller strike; she did not hear or see anything abnormal during the second takeoff and landing. An examination of the airplane by a Federal Aviation Administration inspector revealed wrinkling of the lower firewall and fuselage skin, and both propeller blades bent aft; resulting in substantial damage to the airplane.