  We study the tunneling properties of a cigar-shaped Bose-Einstein condensate
by using an effective 1D nonpolynomial nonlinear Schr\"odinger equation (NPSE).
First we investigate a mechanism to generate periodic pulses of coherent matter
by means of a Bose condensate confined in a potential well with an oscillating
height of the energy barrier. We show that is possible to control the periodic
emission of matter waves and the tunneling fraction of the Bose condensate. We
find that the number of emitted particles strongly increases if the period of
oscillation of the height of the energy barrier is in parametric resonance with
the period of oscillation of the center of mass of the condensate inside the
potential well. Then we use NPSE to analyze the periodic tunneling of a
Bose-Einstein condensate in a double-well potential which has an oscillating
energy barrier. We show that the dynamics of the Bose condensate critically
depends on the frequency of the oscillating energy barrier. The macroscopic
quantum self-trapping (MQST) of the condensate can be suppressed under the
condition of parametric resonance between the frequency of the energy barrier
and the frequency of oscillation through the barrier of the very small fraction
of particles which remain untrapped during MQST.
