Captain reported unusual airframe vibrations at cruise speeds. The flight crew made aircraft maintenance log entries but neglected to fill out the vibration report forms.

Narrative

Maintenance Discrepancy for repeated airframe vibration is on aircraft at time of this flight. On climb out we noticed airframe vibration on departure at 310 KIAS for climb. We slowed to 280 KIAS and vibration went away. Continued climb and transitioned to .79 M where vibration was intermittent. At .78M we did not have vibration and we selected that for continued climb; cruise and descent; transitioning back to 280 KIAS. Maintenance message code sent and Aircraft Maintenance Logbook (AML) entry made. I spoke with mechanics directly on arrival. After entering red eye rest period a Operations Manager called and left a message wanting a report filed so maintenance could start work on aircraft. Time was XA:00 and I did not answer. Upon a wakeful period XD:00 during my rest I checked my phone and saw a company voicemail. After listen I spoke with the Operations Manager who then asked me to interrupt my rest period to file a report; which I filed. I was informed I also needed to file a separate vibration report which was filed. Followed through with the best information we had at the time. Report follow up was impacted with oncoming fatigue following a red eye. I mentioned the AML entry to mechanics but none of us spoke about a vibration report. Other than not completing the report; the details are in the AML.Better combined list for events and report requirements with not links available.