Dear Jason
As I know,the Rayleigh damping have two proportional factor about the mass and stiffness.As you said, Fdamping_i = K_ijbeta_jqdot_j
I think the mass is neglected.If not,
Fdamping_i=M_ijalph_jqdot_j+K_ijbeta_jqdot_j
I am not sure about the question.Hope your reply.
BEST REGARD
Ruiliang.Wang