  Quantum systems can show qualitatively new forms of behavior when they are
driven by fast time-periodic modulations. In the limit of large driving
frequency, the long-time dynamics of such systems can often be described by a
time-independent effective Hamiltonian, which is generally identified through a
perturbative treatment. Here, we present a general formalism that describes
time-modulated physical systems, in which the driving frequency is large, but
resonant with respect to energy spacings inherent to the system at rest. Such a
situation is currently exploited in optical-lattice setups, where superlattice
(or Wannier-Stark-ladder) potentials are resonantly modulated so as to control
the tunneling matrix elements between lattice sites, offering a powerful method
to generate artificial fluxes for cold-atom systems. The formalism developed in
this work identifies the basic ingredients needed to generate interesting flux
patterns and band structures using resonant modulations. Additionally, our
approach allows for a simple description of the micro-motion underlying the
dynamics; we illustrate its characteristics based on diverse dynamic-lattice
configurations. It is shown that the impact of the micro-motion on physical
observables strongly depends on the implemented scheme, suggesting that a
theoretical description in terms of the effective Hamiltonian alone is
generally not sufficient to capture the full time-evolution of the system.
