  Some fast radio bursts (FRBs) exhibit repetitive behaviors and their origins
remain enigmatic. It has been argued that repeating FRBs could be produced by
the interaction between a neutron star and an asteroid belt. Here we consider
the systems in which an asteroid belt dwells around a massive star, while a
neutron star, as a companion of the massive star, interacts with the belt
through gravitational force. Various orbital configurations are assumed for the
system. Direct N-body simulations are performed to investigate the dynamical
evolution of the asteroids belt. It is found that a larger orbital eccentricity
of the neutron star will destroy the belt more quickly, with a large number of
asteroids being scattered out of the system. A non-zero mutual inclination
angle suppresses the ejection rate of asteroids, but it also leads to a
reduction in the collision rate of asteroids with the neutron star since many
asteroids are essentially scattered into the 3D space. Among the various
configurations, a clear periodicity is observed in the collision events for the
case with an orbital eccentricity of 0.7 and mutual inclination of $0^{\circ}$.
It is found that such a periodicity can be sustained for at least 8 neutron
star orbital periods, supporting this mechanism as a possible explanation for
periodically repeating FRBs. Our studies also suggest that the active stage of
these kinds of FRB sources should be limited, since the asteroid belt would
finally be destroyed by the neutron star after multiple passages.
