Why is there increased dryer motor hum while powered by a generator?
Is your generator producing true sine wave, modified sine wave, or square wave output?

The motor's designed to work on sine-wave AC, which is what large generators are happiest producing, and which is generally the most efficient form since all the energy goes into the single frequency and can be easily drawn back out.

Square wave is easier for small alternators to produce, but has a lot of high harmonics which can cause resonance in motors, sometimes to the point of being damaging. Square-wave alternators may also be damaging to some electronics, for similar reasons.

"Modified sine wave" is a compromise between the two -- it adds another few steps between the most-positive and most-negative outputs. This reduces the harmonics to a level that most motors and electronics can handle safely. There are still going to be some harmonics, which may be made audible by the motor, but they shouldn't be strong enough to be damaging.

If you've got a square-wave unit, consider replacing it. If you've got a modified-sine unit and are still having trouble... well, switching to true sine wave will probably solve it, but you might want to get someone with expertise in this system to take a look at your set-up before you commit to that purchase.