Reduced-order model for MEMS PZT vibrational energy harvester exhibiting buckling bistability

Estimating the behaviour of buckling clamped-clamped beams entails solving nonlinear partial differential equations (PDEs). Several techniques are found in the literature that deal with such PDEs; techniques that also take into account initial curvatures and/or imperfections. However, when the system configuration is different from that of one single beam it becomes more involved. In this Letter, a buckling energy harvester is presented. Owing to the nature of its design, a nonlinear differential equation (not a PDE) capable of capturing all the salient characteristics of its behaviour could be developed. The effectiveness of the model is validated using finite element analysis. The energy harvester is designed using the SINTEF piezoVolume process and operated in the d₃₁ mode. With electrical damping only, the device, designed for validation purposes, achieved a power density of 0.13 mW cm^-3 at 3.5 g ms^-2 at 560 Hz and produced d₃₁ open-circuit voltages of 0.6 V.