Mooney pilot reported on departure experiencing a strange shimmy from the aircraft and decided to return to the airport. A gear-up landing occurred although gear lights indicated gear was extended.

Narrative

Preflight: there were no defects found during preflight inspection. Performed as normal; I was feeling fit and safe for the flight. Followed IMSAFE checklist and personal minimum checklistStart up: Followed the checklist. After the second attempt; engine started up by adding more fuel. Reduced power to 1000 RPM. No issues. Taxi: Followed pre taxi checklist. Taxied via Taxiway 1 to runway XX.Run-up: followed check list; I did an extra thorough and longer run up to ensure the plane checked out appropriately due to first flight from annual inspection. No discrepancies with aircraft were encountered. Pre-Take off: Followed pre-take off checklist. Take off roll: Followed take off checklist. Upon rotation a strange 'shimmy' sounding noise started along with shaking; On take off engine temperatures and pressures remained in the green; but at about rotate speed the airplane started shaking. I also felt this could be due to taking off on runway XX as the asphalt is not in the best condition.Once airborne I tapped the brakes to ensure the shaking was not the wheels and continued to climb. The shaking did not stop.Once established a positive rate of climb approx. 500 ft AGL; I went through climb checklist. The shaking of the aircraft became worse.I made the decision to remain in the pattern and pattern and land back on runway XX and initiated turn to cross wind.Preparation for landing: In the downwind I climbed to 1500 AGL just to make sure I had sufficient altitude; performed before landing checklist and personal GUMPS check list. At 140KTS landing gear was extended to slow the aircraft down. I Felt the plane start to slow from gear extension and added 10 degrees of flaps. I then added trim to help with control heaviness. Checked annunciator panel for gear green light and confirmed with green mechanical indication on the floor. Both were green. Made normal radio calls. Reduced power to 1500 RPM about 14 inches manifold pressure. Did personal GUMPS check again. Slowed myself for final. Slowed to 92 knots with 11 inches of manifold pressure. Double checked checklist one more time and final GUMPS check. Until this point there was no gear horn sound at all.Landing: Came over the threshold around 65-75 knots started walking out the power once I knew the runway was made. Waited for the touchdown of the wheels which did not happen.Gear up landing: skidded down runway XX. The first-time gear horn sounded was upon aircraft touching the ground. No time prior to that had the gear horn activated. I then Notified other pilots of the situation and properly shut down the aircraft and double checked and verified the gear handle was in the down position and exited the aircraft.