Abstract: n this paper, fundamental equations of the axisymmetric large amplitude.freevibration for circular sandwich plates are derived by means of Hamilion principle. Inmosi cases, the sandwich plates are composed of very thin faces, then the precedingfundamental equations are simplified considerably. For an illusirative example, a circu-lar sandwich plate with edge clamped but free to slip is considered, and then we gol a pure analytic solution of the axisvmmetric large amplitude free vibration with the aid of the modified iteration method. and derived an analytic relation for the amplitude-frequency response.

Key words: variational inequality, Newton iteration, semilocal convergence, kantorovich theorem, circular sandwich plate, large amplitude, vibration