Design and investigation of a quad-stable piezoelectric vibration energy harvester by using geometric nonlinearity of springs

In this paper, a quad-stable piezoelectric vibration energy harvester induced by the geometric nonlinearity of springs is designed and investigated. The novelty is that by replacing the per-manent magnets with a combination of springs, the system can be effectively protected from electromagnetic interference in the working environment. The innovative design of three hinged springs attached to the tip of the cantilever beam makes the stiffness of the structure inherently nonlinear, which can induce the multi-stability of the system. The Euler-Lagrange equations are applied to establish the governing equation of the energy harvester. The static bifurcation analysis reveals the evolution process of multi-stability. The complex dynamic frequency (CDF) method, an efficient approach to solving strongly nonlinear dynamic problems with multi-well systems, is then applied to deduce the system's amplitude-frequency response. Combinations of theoretical and numerical results show that among a wide frequency bandwidth, the system can exhibit such as single-, double-and quadruple-well periodic motions. Finally, experiments are set up to verify the advantage of inter-well motion on harvesting power. Result shows that geometric nonlinearity can effectively make the energy harvester exhibit multi-stability, generate different movement patterns, and obtain high harvesting power.