  We investigate the short-term dynamical evolution of stellar grand-design
spiral arms in barred spiral galaxies using a three-dimensional (3D)
$N$-body/hydrodynamic simulation. Similar to previous numerical simulations of
unbarred, multiple-arm spirals, we find that grand-design spiral arms in barred
galaxies are not stationary, but rather dynamic. This means that the
amplitudes, pitch angles, and rotational frequencies of the spiral arms are not
constant, but change within a few hundred million years (i.e. the typical
rotational period of a galaxy). We also find that the clear grand-design
spirals in barred galaxies appear it only when the spirals connect with the
ends of the bar. Furthermore, we find that the short-term behaviour of spiral
arms in the outer regions ($R>$ 1.5--2 bar radius) can be explained by the
swing amplification theory and that the effects of the bar are not negligible
in the inner regions ($R<$ 1.5--2 bar radius). These results suggest that,
although grand-design spiral arms in barred galaxies are affected by the
stellar bar, the grand-design spiral arms essentially originate not as
bar-driven stationary density waves, but rather as self-excited dynamic
patterns. We imply that a rigidly rotating grand-design spiral could not be a
reasonable dynamical model for investigating gas flows and cloud formation even
in barred spiral galaxies.
