On the basis of introducing the strain-dependent characteristic of hard-coating material

the dynamic characteristic solution theory of iterative finite element method was derived. Moreover

the processes of calculating natural frequency and vibration response were presented

which can be summarized as: the hard coating material parameters were corrected by the vibration response

and then the dynamic parameters were solved by the iterative solution program. At last

a cantilever beam coated with MgO+Al2O3 hard coating was chosen to display the effectiveness of the proposed method. Considering the strain-dependent characteristic of MgO+Al2O3 hard coating

the natural frequency and vibration response were obtained under different exciting levels and also compared with the relative values obtained by linear calculation. Results show that the hard-coating composite structure cantilever beam displays the soft nonlinear phenomenon

and the resonance responses reduce by 29%-48% compared with linear calculation correspondingly to different exciting levels. This shows that the strain-dependent characteristic of hard-coating material can promote the effect of vibration reduction.