A Tri-Stable Piezoelectric Vibration Energy Harvester for Composite Shape Beam: Nonlinear Modeling and Analysis

To reveal the nonlinear mechanism of the tri-stable piezoelectric vibration energy harvester based on composite shape beam (TPEH-C) and its influence on the system response, the nonlinear restoring force and the nonlinear magnetic force are discussed and analyzed in this paper. The nonlinear magnetic model is acquired by using equivalent magnetizing current theory, and the nonlinear resilience model is obtained by fitting experimental data. The corresponding distributed parameter model based on generalized Hamiltonian variation principle has been established. Frequency response functions for the TPEH-C are derived according to harmonic balance expansion, and the influence of different magnet distances and different excitation accelerations on the response amplitude and bandwidth of the TPEH-C are investigated. More importantly, the correctness of the theoretical analysis is verified by experiments. The results reveal that the spectrum of composite beam shows hard characteristic and the depth of potential well is changed, which provides a new way to ameliorate the potential well of the TPEH-C. A suitable magnet distance enables the TPEH-C to improve the response amplitude and the effective frequency range. The results in this paper have a theoretical guiding significance for the optimal design and engineering application of the TPEH-C.