# Parametric and Experimental Modeling of Axial-Type Piezoelectric Energy Generator with Active Base
## 1 Introduction
In article [20], a cantilever-type generator with an active base was considered. Four cylindrical piezoelements were used in the base. An experimental approach was presented, showing that the maximum output power was 41.8 mW and 7.42 mW for the two types of piezoelectric elements, respectively. In [21], modeling of the cantilever-type PEG with symmetrical and asymmetrical location of proof mass was presented, and the linear theory of elasticity and electrodynamics was used, taking into account the dissipation of energy as well as the equations of motion in the acoustic approximation. The built FE model was numerically realized in the ANSYS software. Reference [22] presented a simulation of two generators having a modification with mass elements symmetrically attached, with respect to the main axis of the generator. It was shown that the maximum output power was 6.97 mW. In [23], FE modeling of a two-axis PEG is considered. The piezoelectric elements were fixed in the form of a bimorph on two cantilevers at the base of the PEG. The calculated output power was 720 mW. The research in [24] considered a cantilever-type PEG having an aluminum base, with piezoelectric elements in the pinched area and an attached mass at the end. The peculiarity of this generator is that there are stopper devices as a component of the device. The authors fixed the movements of the generator base bar. Analytical modeling of the generator was given, and the results of the nonlinear analysis of the output energy characteristics are presented. The output power of the generator was obtained at a level of up to 4.95 mW. Frequencies were considered up to 40 Hz. The article [25] considered a broadband PEG with several degrees of freedom based on five resonant frequencies that were fairly close to each other. The PEG consisted of five end masses, two U-shaped cantilever beams and a straight beam. The selection of resonant frequencies was realized due to the special design of the parameters. The electrical characteristics of the PEG were analyzed through simulation and experiment, confirming that the PEG can effectively expand the operating bandwidth and collect vibration energy at low frequency. Experimental results showed that PEG has five low-frequency resonant frequencies, which are 13, 15, 18, 21 and 24 Hz; under the action of acceleration of 0.5 g, the maximum output power is 52.2, 49.4, 61.3, 39, 2 and 32.1 \(\mu\)W,  
The article [26] considered micro-MEMS PEG, which has a wide frequency band with included stoppers; one and two sides are carefully studied. The results of the experiment showed that the operating band is extended to 18 Hz (30-48 Hz) and the corresponding optimal power ranges from 34 to 100 nW, with a base acceleration of 0.6 g. Mathematical modeling based on the application of differential equations of motion was carried out. In [27], mathematical modeling of PEG was carried out based on the application of [PERSON]'s electromechanical coupling equations. A PEG prototype with two internal single arms was designed, manufactured and experimentally tested. The accuracy of the proposed mathematical modeling was verified by finite element modeling and experimental results. When tested with low harmonic amplitude, the PEG generated 2.48V, 6.21V and 1.55V at three resonant frequencies between 15 and 30 Hz, respectively. A brief analysis of the modifications and studies of PEG shows the following. The authors of the article [28] optimized the power generator and the software for the analysis of FE, performed using the software ANSYS and ACELAN. The optimal design was based on matching the resonant frequency of the device with the excitation frequency of the environment [28]. In the article [29], a packet-type piezoelectric energy generator was studied. An experimental setup was used and measurements of the response of a multilayer piezoelectric stack in an energy harvester were described. Paper [30] proposed a single-degree fractal structure system for energy collection.