# Parametric and Experimental Modeling of Axial-Type Piezoelectric Energy Generator with Active Base
## 2 Description of Model Parameters and Electric Scheme  
An axial piezoelectric transducer for converting mechanical energy into electrical energy contains a base plate (7) in the form of a rigid beam structure made of elastic material, on which piezoelectric bimorph (2, 3) elements are glued (see Figure 1). One end of the beam structure is bolted (9) to the base (4) by Fixing supports (5). To the other end, at the base, piezoelectric elements of the cylindrical type (1) are fixed coaxially with the base bar through an L-shaped bar (6). An additional proof mass M (8) is located between the edge of the base, fixed with a bolt (9) and the piezoelectric elements (3).  
Thin symmetric piezoelectric elements (PE) are polarized in thickness. They are glued to the base console and are arranged in a row (see Figure 2). Characteristics of the dimensions of the PEG elements are presented in the Table 1, the properties of the elements are presented in the Tables 2-4 show the mechanical properties of PE materials. In the full-scale model, we used PE made of CTS-19 material produced at Piezopribor LLC of the Southern Federal University (Rostov-on-Don, Russia). In the simulation, the parameters of materials with equivalent properties presented in [39] are used.  
Figure 1: Structure scheme of PEG with proof mass: 1—piezocylinder; 2,3—plate piezoelectric elements; 4—rigid base of the generator; 5—PEG fixing supports; 6—L-clamping bar; 7—base; 8—proof mass; 9—screw.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No.** & **Name** & \multicolumn{6}{c}{**Geometric Parameters, mm**} \\ \hline
1 & Piezocylinder & R\({}_{\rm PC}\) & 14 & h\({}_{\rm PC}\) & 12.5 & & \\
2, 3 & Piezoelements & L\({}_{\rm P}\) & 20 & b\({}_{\rm P}\) & 15 & h\({}_{\rm P}\) & 0.5 \\
4 & Rigid base & L & 300 & B & 50 & H & 25 \\  & & t & 2 & & & \\
5 & Fixing supports & L\({}_{\rm I}\) & 50 & b\({}_{\rm I}\) & 25 & h\({}_{\rm I}\) & 25 \\  & & t & 2 & & & \\
6 & L-clamping bar & L\({}_{\rm L}\) & 74 & b\({}_{\rm L1}\) & 25 & b\({}_{\rm I2}\) & 24 \\  & & t\({}_{\rm I}\) & 15 & h\({}_{\rm L}\) & 2 & & \\  & & d\({}_{\rm P}\) & 10 & & & \\
7 & Base & L\({}_{\rm b}\) & 260 & b\({}_{\rm m}\) & 14 & h\({}_{\rm m}\) & 1.5 \\
8 & Mass & L\({}_{\rm m}\) & 16 & b\({}_{\rm m}\) & 10 & h\({}_{\rm m}\) & 4 \\
9 & Screw & L\({}_{\rm d}\) & 44 & R\({}_{\rm d}\) & 13 & & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Geometric characteristics of the dimensions of PEG elements.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**N** & **PEG Element** & **Material** & \(\rho\)**, kg/m\({}^{3}\)** & \({\bf E\times 10^{11}}\)**, Pa** & **v** \\ \hline
1 & Piezocylinders & CTS-19 & 7280 & - & 0.33 \\
2, 3 & Piezoelements & CTS-19 & 7280 & - & 0.33 \\
4 & Rigid base & duralumin & 2600 & 0.7 & 0.33 \\
5 & Fixing supports & duralumin & 2600 & 0.7 & 0.33 \\
6 & L-clamping bar & steel & 7700 & 2.1 & 0.33 \\
7 & Base & duralumin & 2600 & 0.7 & 0.33 \\
8.1 & Proof mass & plastic & 1600 & 0,06 & 0.33 \\
8.2 & Proof mass & duralumin & 2600 & 0.7 & 0.33 \\
8.3 & Proof mass & steel & 7700 & 2.1 & 0.33 \\
9 & Screw & steel & 7700 & 2.1 & 0.33 \\ R & Active electric load & resistor & & \(1\,\mathrm{k}\Omega-2\,\mathrm{M}\Omega\) & \\  & damping value & & & \(\xi=0.031\) & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mechanical properties of the materials.  
Figure 2: Electric scheme of axial-type PEG under active electric load and structure scheme of PEG with proof mass: 1—piezoelectric cylindrical element; 2—piezoelectric bimorph element; 3—substrate; 4—proof mass; 5—clamping bar of PEs (1) fixing; 6—place of PEG fixing. (B) is the movable base; p is the PE’s polarization direction.