We present measurements of three-particle correlations for various harmonics
in Au+Au collisions at energies ranging from $\sqrt{s_{{\rm NN}}}=7.7$ to 200
GeV using the STAR detector. The quantity
$\langle\cos(m\phi_1+n\phi_2-(m+n)\phi_3)\rangle$ is evaluated as a function of
$\sqrt{s_{{\rm NN}}}$, collision centrality, transverse momentum, $p_T$,
pseudo-rapidity difference, $\Delta\eta$, and harmonics ($m$ and $n$). These
data provide detailed information on global event properties like the
three-dimensional structure of the initial overlap region, the expansion
dynamics of the matter produced in the collisions, and the transport properties
of the medium. A strong dependence on $\Delta\eta$ is observed for most
harmonic combinations consistent with breaking of longitudinal boost
invariance. Data reveal changes with energy in the two-particle correlation
functions relative to the second-harmonic event-plane and provide ways to
constrain models of heavy-ion collisions over a wide range of collision
energies.