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A circular laminated plate manufactured by a brass plate and two piezoelectric plates is an effective structure in piezoelectric actuators and energy harvesters. An experimentally modeling approach is proposed to derive a simple equivalent model of the plate. The laminated plate with the center mass is approximated by a single-degree-of-freedom nonlinear oscillator. A completely non-parametric identification method based on the Hilbert transform is applied to identify the nonlinear terms. Under the experimental conditions, the basement excitation is used in the experiment and the stiffness and damping functions can be estimated. The results demonstrate that the stiffness function has the soft nonlinear characteristic under small displacements but the hard nonlinear characteristic under large displacements. The damping function is also nonlinear. It decreases with the increasing speed and tends to constant for the sufficiently large speed.