Modeling and Characteristic Analysis of Combined Beam Tri-Stable Piezoelectric Energy Harvesting System Considering Gravity

The emergence of the vibration energy harvesting system makes it possible for wireless monitoring nodes in coal mines to realize self-power supply. In order to reveal the influence of gravity effect on the response characteristics of the combined beam tri-stable piezoelectric energy harvesting system (CTEHS), the system’s nonlinear magnetism is calculated according to the principle of point magnetic charge dipole, and the system’s nonlinear resilience is obtained through experimental measurements and nonlinear fitting methods. Based on the Lagrange equation, the system’s electromechanical coupling motion model considering gravity is established. The system’s motion equation is solved numerically based on the Runge–Kutta algorithm, and the effects of the end magnet mass and the initial vibration point on the bifurcation behavior, potential energy, and system output performance are investigated by emulation and experiment. The research shows that the magnet’s gravity effect causes a change in the stable equilibrium position and the system’s motion state and also causes the system to generate additional gravitational potential energy, which leads to a potential asymmetric well of the system. Under the consideration of magnet gravity, the appropriate end magnet mass and initial vibration point can not only reduce the system’s requirements for external excitation strength but also effectively improve the system’s response and output. This research provides a new theoretical basis for the optimal design of the tri-stable piezoelectric energy harvesting system.