Environmental vibration energy is a kind of renewable and clean energy with abundant reserves and wide distribution. Through energy harvesting technology，the mechanical energy in the environment is converted into electrical energy to power low-power electronic devices and wireless sensor networks，which is an effective solution to break the limitations of traditional power supply methods. In this paper，the bursting oscillation and energy capture efficiency of a mechanical nonlinear multistable piezoelectric cantilever beam device are studied under low frequency excitation. By analyzing the potential energy of the system，it can be seen that the system has multi-stable characteristics with the change of system parameters. According to the fast and slow dynamic analysis method，the external excitation term is regarded as a slow variable and control parameter to adjust the dynamic behavior of the fast subsystem，and the time history diagram，phase diagram and transition phase diagram of the system are obtained. The motion state and energy capture performance of the system under low frequency excitation are analyzed by numerical method. The results show that the system exists bursting oscillation under low frequency excitation，and the system has good energy capture characteristics when the system is bistable. In addition，the time-delay feedback control can control the clustering phenomenon and ensure the stable operation of the system.