  With the help of the linearized perturbation theory, the collective beam
instability due to the space charge, modelled by the Vlasov-Poisson equation,
is well studied in the former research theoretically in a general sense [Chao
Li and R. A. Jameson PRAB, 21, 024204 (2018)], where the related instability is
depicted by the "structure resonance". As an extension of the theoretical
study, this paper aims to verify the validity of the structure resonance with
numerical simulations and to show the basic principles which interpret the
interaction between structure resonance and beam in a general sense. It is
found that the reaction of beam to the structure resonance ($n\sigma\approx
180^\circ$) differs for the cases with $n= 0$ and $n\ne 0$ stop bands. The
non-resonant "plasma oscillation" is also revisited; the "phase space mixing",
lying in the transient plasma oscillation, is the mechanism that ties the
resonant effects, non-resonant effects and macroscopic beam phenomena together.
