In the framework of A Multi-Phase Transport (AMPT) model, multi-particle azimuthal cumulant method is used to calculate linear and mode-coupled contributions quadrangular flow harmonic ($v_{4}$), response coefficient as a function centrality in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200, 39, 27 19.6 GeV. This study indicated that $v_{4}$ are sensitive beam energy change. Nevertheless, c...