I have a Whirlpool electric clothes dryer and it is under 5 years old. When it is drying it makes a "whirling sound" that is especially loud from the outside where it is vented. My neighbor is constantly complaining about it. We shoved a large rock up in the vent from the outside and that helped a lot, but the clothes did not dry properly as they should have on the normal setting with the normal amount of clothes that I always dry.
Absolutely do not block the vent - this could cause a fire!
The first thing to check is that your duct is free of lint and other debris. If it is a plastic duct then I wouldn't even bother cleaning it and instead would replace it with a metal one. A rigid duct line is probably better than a flexible one but is a bit more difficult to work with.
Check for any unnecessary bends or kinks in the line - the straighter the better as bends restrict the airflow and result in additional noise. If it is a collapsible/flexible duct, make sure it is fully extended and trim off any excess ducting.
If possible you might consider relocating the exhaust further away from you neighbor.
Do NOT block the vent. Stuffing something into it is a sure way of setting your home on fire in only a short time. And your clothes won't dry either. Ok, when the fire starts, things will get hot, but then the fire company will wet it all down. It won't be a happy occasion.
Seriously, what I'd offer is to create a muffler. I'd build a large box around the end of the vent that can muffle the sounds. Put some holes in the box, that do not aim at your neighbor. Make it so you can open it and clean out any lint that accumulates. Make sure you check this periodically.
Generally to quiet exhaust flows you add a big expansion area into the pipe, like a car muffler or even a gun silencer. I don't think this is a good idea for a clothes dryer, as it will accumulate lint, which can become a fire hazard.
I'd suggest using some sort of a structure to block the direct "line of sight" between the exhaust vent and your unsettled neighbor. This could be a section of fence or a shrub. be sure to keep a couple of feet of clearance between the exhaust vent whatever you put out there so that you allow good airflow.
If all else fails, bring the neighbor some cookies and some ear plugs.
As others have said, get that rock outta there post haste!
I am a neighbor with this problem which became a huge issue and not addressed immediately. Solution: Rigid pipe, only two bends, short as possible. Moved exit hole to grassy backyard rather than aimed at a concrete driveway that amplified sound bounced on neighbors house. It was the right thing to do. Fixed it. Also put a hood on exit hole to direct sound to the ground rather than the just the flaps - dryer works faster now and it lowered bill. We also agreed not to do laundry after 10pm because its not a hard thing to do and saves cop calls!