Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Maintenance; Deviation / Discrepancy - Procedural Published Material / Policy
Aircraft Aircraft Damaged; General Flight Cancelled / Delayed; General Maintenance Action
Procedure; Aircraft
[The First Officer] and I flew Aircraft X from ZZZ to ZZZ1. During the cruise portion of the flight; we both felt the airplane vibrating a bit more than usual. We looked around near the engine and props to see if anything from that area would cause the vibration and also looked at the engines performance page on the Multi Function Display screen to see if there were any abnormalities. Everything was performing normally and we decided to scan everything through our window starting from the inboard part of the wing; then the engine and the outboard part of the wing. We ensured the flaps were up as well. We then looked at the horizontal stabilizer and saw it shaking up and down as if the plane was hitting turbulent air. It looked a bit more than what we usually see. We both agreed we could continue safely to ZZZ1 but would divert and land immediately if we felt the vibration get any worse. As we continued to fly the vibration was intermittent. There was not a repetitive pattern rather the plane would vibrate for 10-20 seconds and then return to a normal vibration. During our descent the vibration was more frequent; instead of intermittent; but was not more intense. Once we parked at the gate in ZZZ1; I examined the rear section of the aircraft and called maintenance to request someone come look with me. During the inspection I saw that a screw had pierced through the plate which is connected to the horizontal stabilizer and the bottom of the fuselage. We brought the plane to the maintenance hangar and I asked [the] ZZZ1 Maintenance Manager to look at the plane with me and I told him about what I found. As he inspected the screws in the plate on the other side of the fuselage a screw fell out in his hand. I then called Maintenance/Operations Control and told them what was happening since the plane was going to be written up and our next flight was going to be delayed.
Air Taxi Captain reported excessive vibration on descent which caused the aircraft to be removed from service at the destination airport.