The nonlinear characteristics of a simply-supported three-layer circular piezoelectric plate-like power harvester near resonance are examined in the paper, where the energy-scavenging structure consists of two properly poled piezoceramic layers separated by a central metallic layer. The structure is subjected to a uniform harmonic pressure on the upper surface. Nonlinear effects of large deflection near resonance to induce the incidental in-plane extension are considered. Results on output powers are presented, which exhibit multi-valuedness and jump phenomena.