Force and stability mechanism analysis of two types of nonlinear mono-stable and multi-stable piezoelectric energy harvesters using cantilever structure and magnetic interaction

Nonlinear mono-stable and multi-stable piezoelectric energy harvesters have attracted a lot of attention owing to their broadband frequency spectra and excellent energy harvesting performance. Herein, two types of nonlinear mono-stable, bi-stable, tri-stable, and quad-stable piezoelectric energy harvesters using cantilever structure and magnetic interaction are compared and analyzed. Based on the magnetizing current method, the magnetic force equations are obtained. Calculation results demonstrate that the stability of these harvesters is dependent on the equivalent linear elastic force and the vertical magnetic force. The equilibrium point occurs when the equivalent linear elastic force equals to the vertical magnetic force. The relationship between the number of stable equilibrium points E _S and the number of the intersections of the two force curves N _I is that E _S= (N _I + 1)/2. Experiments are carried out to verify the equivalent linear elastic force, vertical magnetic force, and the number of stable equilibrium points of the fabricated prototypes. The experimental results are consistent with the calculated results, which verifies the correctness of the stability mechanism. Moreover, it is found that the stability mechanism is also applicable to the harvesters with more stable equilibrium points, such as penta-stable and hexa-stable harvesters. This work reveals the stability mechanism of nonlinear mono-stable and multi-stable energy harvesters using cantilever structure and magnetic interaction, and provides technical methods for the design of multi-stable energy harvesters.