Nonlinear Dynamic Analysis of Bistable Piezoelectric Energy Harvester with a New-Type Dynamic Amplifier

Abstract

A distributed parametric mathematical model of a new-type dynamic magnifier for a bistable cantilever piezoelectric energy harvester is proposed by using the generalized Hamilton principle. The new-type dynamic magnifier consists of a two-spring-mass system, one is placed between the fixed end of the piezoelectric beam and the L-shaped frame, and the other is placed between the L-shaped frame and the base structure. We used the harmonic balance method to obtain the analytical expressions for the steady-state displacement, steady-state output voltage, and power amplitude of the system. The effect of the distance between the magnets, the spring stiffness ratio and mass ratio of the two dynamic magnifiers, and the load resistance on the performance of the harvester is investigated. Analytical results show that compared with the bistable piezoelectric energy harvester with a typical spring-mass dynamic magnifier, the proposed new-type energy harvester system with a two-spring-mass dynamic magnifier can provide higher output power over a broader frequency band, and increasing the mass ratio of the magnifier tip mass to the tip magnet can significantly increase the output power of the BPEH + TDM system. Properly choosing the stiffness ratio of the two dynamic amplifiers can obviously improve the harvested power of the piezoelectric energy harvester at a low excitation level.

Dynamic Characteristic Analysis of Tri-Stable Piezoelectric Energy Harvester with Double Elastic Amplifiers

“…In the steady state, all derivatives of time are 0. Therefore, the analytical expressions of displacement amplitude and voltage amplitude of the system can be obtained by using formulas (19)(20)(21)(22) as follows:…”

“…At present, most of the studied multi-stable piezoelectric energy harvesters are fixed on rigid bases. Once the positions of cantilever beams and magnets are fixed, it will be difficult to adjust the frequency bandwidth of piezoelectric harvesters to match the external excitation frequency by changing the relative positions between magnets, so as to realize large-scale inter-well motion [21][22]. Considering the above shortcomings of rigid base and to further improve the power output of multi-stable piezoelectric energy harvester under weak excitation intensity, researchers introduce elastic amplifier base into the structure of multi-stable piezoelectric energy harvester [23].…”