  The properties of the nonlinear frequency shift (NFS) especially the fluid
NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion
species plasmas have been researched by Vlasov simulation. The pictures of the
nonlinear frequency shift from harmonic generation and particles trapping are
shown to explain the mechanism of NFS qualitatively. The theoretical model of
the fluid NFS from harmonic generation in multi-ion species plasmas is given
and the results of Vlasov simulation are consistent to the theoretical result
of multi-ion species plasmas. When the wave number $k\lambda_{De}$ is small,
such as $k\lambda_{De}=0.1$, the fluid NFS dominates in the total NFS and will
reach as large as nearly $15\%$ when the wave amplitude $|e\phi/T_e|\sim0.1$,
which indicates that in the condition of small $k\lambda_{De}$, the fluid NFS
dominates in the saturation of stimulated Brillouin scattering especially when
the nonlinear IAW amplitude is large.
