Introducing Lindhard potential to describe crystalline undulator radiation,the particle motion equation is reduced to the Duffing equation with a hard-spring properties in the classical mechanics frame and the dipole approximation. The main resonance and the super-harmonic resonance are analysed by the multi-scale technique;the nonlinear behaviours on a particle motion are discussed near resonance line;the critical parameter ac and system stable condition are derived. Because the critical condition is related to the parameters of the system,then these parameters are regulated suitably,an instability can be avoided in principle.Thus the effective output of X-laser or γ-laser can be assured. The theoretical analysis is provided to obtain the short wavelength laser.