  We present a numerical analysis of the particle creation for a quantum field
in the presence of time dependent boundary conditions. Having in mind recent
experiments involving superconducting circuits, we consider their description
in terms of a scalar field in a one dimensional cavity satisfying generalized
boundary conditions that involve a time-dependent linear combination of the
field and its spatial and time derivatives. We evaluate numerically the
Bogoliubov transformation between {\it in} and {\it out}-states and find that
the rate of particle production strongly depends on whether the spectrum of the
unperturbed cavity is equidistant or not, and also on the amplitude of the
temporal oscillations of the boundary conditions. We provide analytic
justifications for the different regimes found numerically.
