When you are using the winch, the chassis will be under tension, i.e being stretched, which is the opposite to what happens when you collide with stuff front on.
The reason the bull bar vibrates is that it is effectively cantilevered off a chassis made of "thin" panels. Think wobble board (Rolf Harris's muscical instrument for the ancient). This is what gives its "crushability" for the safety rating. If you don't want it to wobble, you would need to go back to a vehicle with a solid chassis.
For most people, who spend their 99% of driving on the black stuff, end of story. Use mounting springs (and mass blocks) for stuff mounted on it. Or change the suspensions and/or drive slower.
Our 6/9db aerial with one or two loading coils in the shaft changes vibration modes depending on the shaking off the bull bar(speed and conditions).
Now, if you are hammering 100kms of corrugations too and from work each day and think it is getting really bad after 5 years, then have a look at the chassis at the various points where it attaches and see if it is cracked, or permanently deformed, or even just shedding or crazing of the coating. Anything you do to beef it up, like running a welding bead, will compromise any safety rating. My 2c is that you would see "damage/signs" at the shock absorber mounting points first. And you'll probably need a new seat.