  We present a general analytical approach to investigate relativistic
corrections in the dynamical Casimir effect (DCE). Particularly, we discuss the
behavior of the additional frequency bands that appear in the spectral
distribution of the created particles when the first relativistic corrections
are taken into account. We do that in the context of circuit QED, by analyzing
the setup used in the first measurement of the DCE, where a system with a
time-dependent boundary condition simulates the mechanical motion of a single
mirror in 1+1 dimensions. Our method is applicable to a large class of systems
with oscillatory time-dependent parameters and can be generalized to higher
dimensions and other fields.
