I have been through following papers for research:
1)http://cdsads.u-strasbg.fr/cgi-bin/nph-iarticle_query?1990ApJ...362..584M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf
2)https://arxiv.org/pdf/gr-qc/9905054.pdf
Conclusion of the second paper given above states the following:
"
In this case the
external action (the gravitational wave) amounts to a time variation of the frequency
parameter of the initial system (charged particles in a magnetic field), so that in the
overall system the equilibrium at rest (x
1 = 0) is unstable. Any deviation from this
state, however small, is sufficient to lead to a rapidly increasing displacement along
the peprendicular direction (Landau and Lifshitz 1976). Further analysis shows that,
in any of the above propagation cases, the overall result would be an exponential
increase of the perpendicular energy of the particles involved in this interaction, as a
function of the affine parameter and, hence, of their proper-time as well.
"
From the conclusion I can understand that gravitational blueshift may be the reason for increasing frequency but what could be the reason for perpendicular displacement of particles and exponential increase in perpendicular energy?