We perform oscillatory shear simulations to determine the loss modulus for three solids with identical interaction yet distinct structures: ordered, random, and glassy alloys. Random and glassy alloys show more pronounced high-frequency loss in the THz regime than the ordered alloy. Ordered and random alloys exhibit a power-law decay in damping strength as frequency decreases over nearly five decades. Glassy alloy, with a limited frequency range of power-law decay, retains significant damping at low frequencies extending down to $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$ due to slow irreversible deformation of local clusters.