I'm going to guess that this is what was intended
wn = 196570;
r = 6351.43;
chi = 0:0.1:2;
phim = 1;
ke = 1.134;
w = 1./(wn.^2.*sqrt(1+(r.*chi).^2)).*sqrt((1-(1+2*phim.*r).*chi.^2).^2 + ((1+ke.^2).*r.*chi + 2*phim.*chi - r*chi.^3).^2);
plot(chi,w)
compare as needed.