Hawker 800 Captain reports banging noises coming from the rear of the aircraft during climb and initially believes the passengers are responsible. When a passenger comes forward to question the loud noises an impending generator failure is suspected. At the top of descent a generator failure is annunciated and the remainder of the descent and approach is flown with the affected engine at idle.

Narrative

Approximately 10 minutes after takeoff; during climb; we started to hear repeated low frequency banging noises from the back of the aircraft; but didn't think much of it as it sounded just like the passengers slamming tables and drawers etc. Another 5-10 minutes later the banging sounds gradually became more of a hum and constant vibration in the entire airframe could be felt. A passenger came up to tell us that there was an unusual noise and vibration coming from the back of the aircraft. All engine indications were normal. Based on past experience I suspected an impending generator failure. Being nearly halfway to the planned destination on a short flight and with no good alternate airports in the area; we decided to continue to our destination. I phoned Maintenance Control and Flight Tracking to inform that we would need maintenance upon landing. The vibration and humming noise persisted. Around the top of descent the GEN 1 FAIL light came on. Appropriate abnormal checklist was completed. Vibrations from the #1 engine continued to increase and we debated shutting down the engine to avoid possible collateral engine damage. We decided to leave the engine at idle where the vibrations were more tolerable and engine thrust still available if needed. An emergency was not declared. The descent was in IMC and light icing conditions. We accepted vectors for a straight in ILS. Upon exiting icing conditions during the descent non-flying pilot started the APU for backup generator power. Pilot flying flew the ILS with the #1 engine at idle thrust to a normal landing. Maintenance found the #1 starter/generator had a disintegrated shaft bearing.