Quantum waveguide theories have been successfully applied to various time-independent ballistic transports in mesoscopic structures, including typically the Aharonov-Bohm rings. Here, we consider the quantum transport along the one-dimensional electron structures driven by time-dependent external fields, typical the open mesoscopic rings threaded by time-periodic magnetic fluxes. Based on the well-known Floquet theorem we effectively separate the time and space variables in the transport equations. As a consequence, the time-dependence behaviors can be characterized by the so-called Floquet energies and the usual quantum waveguide theory (only involving with elastic scatterings) could be generalized to treat the situations with various inelastic scatterings between different Floquet energy sidebands. Our numerical results show clearly that, due to the interaction between the electrons and the applied oscillating fields (i.e., time-dependent fluxes), transmission resonances can be induced by means of photon emissions and absorptions. The influence of the amplitude of the additional static magnetic flux on these photon-assisted tunnelings are also investigated.