"What I do not understand is why [several things]..."
"... these research questions appear laughable."
How about before declaring these questions laughable, you try a little harder to understand why they are interesting? For instance, the fact that we don't have computers powerful enough to simply simulate the question being asked provides one clue of a possible reason why this is more interesting than you think.
Either one of "I don't understand this research" or "this research is laughable" I might accept from a given person, but the combination is unpleasant.
I have a degree in physics, so I guess it was a mistake to leave out the (two) punchlines and leave them implied:
1. "absorb vibrations by trapping pressure waves" is a meaningless concept in physics. Sponges, rubber, styrofoam, springs and crumpled paper all "absorb vibration" in the same way - converting mechanical energy into heat. Apart from a rather pedantic system in which somehow air pressure is used to add angular velocity to a flywheel, there is no sense in which vibrations are "stored". There is also the case of an irreversible deformation, as when a car crumples. And in that case, the object would become monotonically less capable of absorbing energy - a curve that would be easy to measure (place crumpled paper in a vice, repeatedly attempt to squeeze a bit, measure maximum and minimum circumference, repeat, graph)
2. Thermodynamically, any excess energy is going into heat. Period. This could be tested by very carefully measuring the temperature of the crumpled paper before and after being deformed several times, as with the vice above. Eventually (and with paper, sooner rather than later) there's going to be microscopic breakdown at the fiber and even molecular levels, and that increase in entropy must be factored in, too. (Now that is an interesting experimental challenge: how to measure the "looseness" of paper fiber in a crumpled sheet. There are some easy destructive ways but I cannot think of any non-destructive ones.)
So yes, I call shenanigans on this professor and, apart with the (already admittedly) interesting problem of describing the geometry of particular crumples, I think his research is laughable. Although I would enjoy being shown how I am in error, if that be the case.
"... these research questions appear laughable."
How about before declaring these questions laughable, you try a little harder to understand why they are interesting? For instance, the fact that we don't have computers powerful enough to simply simulate the question being asked provides one clue of a possible reason why this is more interesting than you think.
Either one of "I don't understand this research" or "this research is laughable" I might accept from a given person, but the combination is unpleasant.