Effect of Blue-Shifted GWs on Particles

[Gravitoastronomy]

I assume that the energy transported by a gravitational wave is dependent on its frequency, just like EM waves. If that is the case, let's imagine a particle traveling at relativistic speeds relative to the lab frame. Let's imagine the interaction of this relativistic particle with a gravitational wave of lab's energy E traveling with speed c and in direction opposite to that of the particle with respect to the lab's frame. With respect to the particle system of reference, the GW will be blue-shifted so its energy could be much higher. Would this high energy interaction produce some effect different to the interaction of a low-energy GW and a "at-rest" particle? Could these hypothetical effects be detected when considering cosmic rays and the sort (ultrarelativistic particles) and background GW interactions?

 

[mfb]

The intensity increases from "extremely tiny" to "still extremely tiny".

LIGO accelerated to relativistic speeds would see a difference. Particles flying through space don't care. You could hope for particle-graviton interactions, but those would still have negligible impact on the particles for every realistic setup.