  We present 3D smoothed particle hydrodynamics simulations of protoplanetary
discs undergoing a flyby by a stellar perturber on a parabolic orbit lying in a
plane inclined relative to the disc mid-plane. We model the disc as a mixture
of gas and dust, with grains ranging from 1 {\mu}m to 10 cm in size. Exploring
different orbital inclinations, periastron distances and mass ratios, we
investigate the disc dynamical response during and after the flyby. We find
that flybys induce evolving spiral structure in both gas and dust which can
persist for thousands of years after periastron. Gas and dust structures
induced by the flyby differ because of drag-induced effects on the dust grains.
Variations in the accretion rate by up to an order of magnitude occur over a
time-scale of order 10 years or less, inducing FU Orionis-like outbursts. The
remnant discs are truncated and warped. The dust disc is left more compact than
the gas disc, both because of disc truncation and accelerated radial drift of
grains induced by the flyby.
