Date: 201812
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: VMC
Aircraft: B737 Next Generation Undifferentiated
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
Airspace: Class B ZZZ
ATC / advisory: Tower ZZZ
Aircraft component: Nose Gear Door
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Less Severe
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport; General Maintenance Action; General Flight Cancelled / Delayed
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: At rotation we heard a loud bang and then a vibration began. As we accelerated the vibration increased. I continued with the profile and began to accelerate at 3000 feet. As the AC (aircraft) accelerated we discussed limiting our speed to 250 and 10;000 feet. We discussed returning to the field. We decided to return and I transferred AC control and radios to [my FO (First Officer)]. I contacted Dispatch. I informed him of the situation and decided that I would like [ground personnel] to evaluate the AC on landing for any damage that might hinder our taxi in and that I needed overweight landing data. The Dispatcher asked if I wanted to burn fuel and I stated we would have to hold over two hours to burn fuel to be at max landing weight. My concern was that whatever was causing the vibration might increase damage to the AC and create a less safe situation. I contacted the flight attendants and asked if they heard or felt the vibration. They said that had. I gave them [a briefing] and asked that they make a PA to inform the passengers that we were returning. [The FO] and I prepared for the approach. Completed the Descent Checklist and decided to configure early in case there was some sort of gear or configuration issue. We had a moment so I made a PA informing the passengers of our situation and that we were making a normal landing. We advised the tower on check in that we wanted to stop on the runway to be evaluated by [ground personnel] for damage and potentially hot brakes. I was PF (Pilot Flying) and made a normal landing. Stopped straight ahead; did not set the brakes and [ground personnel] evaluated our AC. We advised Tower our desire to taxi to a gate but that we didn't have one yet. They held us short of [the runway] and advised us that Company wanted to taxi to [a specific] gate. We parked; completed the Parking Check and Maintenance showed us that the actuation rod for the left nose gear door had sheared. [Chief Pilot] met us at the AC and evaluated or ability to continue. The [FO] and I discussed it and decided we were able to continue.


Second narrative: After the CA (Captain) called for gear up and I selected it up; there was a louder than normal clunk while the gear was retracting. At this point; the aircraft started to vibrate and was unusually loud. It didn't hinder cockpit communications noticeably since we were both using noise canceling headsets and the flight interphone system. We climbed out at V2+20 and the noise/vibration remained constant. Once we hit 3000 feet MSL and started to accelerate the noise and vibration got worse. The CA was new to the airplane and asked what I thought. While we had no abnormal cockpit indications it was clear something was wrong with the aircraft. We asked to level off there and determined that a return to [departure airport] was the best plan. By the time we went outside to look at the aircraft; maintenance had already identified a sheared nose gear door arm on the aircraft's left side that prevented the gear door from closing. This was the cause of the vibration; since it didn't close when we put the gear up. Nothing else unusual was relayed to us.


Synopsis: B737NG flight crew reported returning to departure airport after experiencing vibration from the nose gear door.