A consistent geometrically nonlinear model of cantilevered piezoelectric vibration energy harvesters. (10th November 2020) - Li, Jiajie; He, Xuefeng; Yang, Xiaokang; Liu, Yufei
Highlights: A novel geometrical nonlinear model for piezoelectric energy harvesters is proposed. The high order terms of the derivative of deflection are consistently handled. The effects of geometrical nonlinearity on the boundary conditions are considered. The proposed model shows better agreement with experiments on the output voltage in comparison with the common geometrical nonlinear model. . Graphical abstract: Image, graphical abstract Abstract: Current theories inconsistently handled the geometrical nonlinearity of cantilevered piezoelectric energy harvesters (PEHs) in two aspects: first, some of the high order terms of the first derivative of deflection were unintentionally omitted in deriving the governing equations; second, the effect of the geometrical nonlinearity on the motion of the tip mass was neglected. In this paper, a consistent geometrically nonlinear model (CGNM) was derived by neglecting the fourth and higher order terms of the first derivative of deflection in the governing equations, and by considering the effect of geometrical nonlinearity on the motion of the tip mass. For a flexible unimorph cantilever, the errors caused by either of the inconsistent treatments of the geometrical nonlinearity were numerically analyzed, respectively, and the theoretical and experimental results showed that both of them have remarkable effects on the simulation accuracy under harmonic base excitations with the amplitudes of 1.5 g and 2.0 g (g = 9.81 m s −2 ). Under excitations of different levels, the voltage across a 500 kΩ resistor worked out from a published geometrically nonlinear model (GNM) and the proposed CGNM were compared with experiments. The CGNM is more accurate than the GNM in the prediction of the root mean square (RMS) voltage at the resonant frequency, especially under high-level excitations. Numerical simulations show that the optimum load resistance increases and the resonant frequency decreases when the excitation level increases due to the geometrical nonlinearity. The model may be used to predict the responses of cantilevered PEHs experiencing large amplitude vibrations.