# Design of an Energy Harvester Based on a Rubber Bearing Floating Slab Track
## 4 Performance Comparison of Energy Harvesters  
### Numerical Model  
In the COMSOL Multiphysics software, the output voltage of each energy harvester was simulated by using the coupled physical field of solid mechanics and electrostatic. In order to simulate the voltage output characteristics of energy harvesters under the same stress state, energy harvesters of different structural types were embedded in the cylindrical concrete structure with a height of 50 mm and a diameter of 32 mm, where the concrete strength grade is C35. The overall model is shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Unit** & **Description** \\ \hline \(\mathrm{S}_{33}^{\mathrm{E}}\) & 20.7 \(\times\) 10\({}^{-12}\) & m\({}^{2}\)/N & Flexibility coefficient \\ \(\mathrm{d}_{33}^{\mathrm{E}}\) & 593 \(\times\) 10\({}^{-12}\) & C/N & Piezoelectric strain constant \\ \(\varepsilon_{73}^{\mathrm{E}}\) & 3400 & / & Relative dielectric constant \\ \(\mathrm{C}_{1}^{\mathrm{E}}\) & 1.27 \(\times\) 10\({}^{11}\) & N/m\({}^{2}\) & Elastic coefficients in direction 1 \\ \(\mathrm{C}_{12}^{\mathrm{E}}\) & 8.02 \(\times\) 10\({}^{10}\) & N/m\({}^{2}\) & Elastic coefficients in direction 2 \\ \(\mathrm{C}_{13}^{\mathrm{E}}\) & 8.47 \(\times\) 10\({}^{10}\) & N/m\({}^{2}\) & Elastic coefficients in direction 3 \\ \(\mathrm{C}_{33}^{\mathrm{E}}\) & 1.17 \(\times\) 10\({}^{11}\) & N/m\({}^{2}\) & Elastic coefficients in direction 4 \\ \(\mathrm{C}_{44}^{\mathrm{E}}\) & 2.30 \(\times\) 10\({}^{10}\) & N/m\({}^{2}\) & Elastic coefficients in direction 5 \\ \(\mathrm{C}_{85}^{\mathrm{E}}\) & 2.30 \(\times\) 10\({}^{10}\) & N/m\({}^{2}\) & Elastic coefficients in direction 6 \\ \(\mathrm{C}_{66}^{\mathrm{E}}\) & 2.35 \(\times\) 10\({}^{10}\) & N/m\({}^{2}\) & Elastic coefficients in direction 7 \\ \(\mathrm{e}_{31}\) & 17.03 & C/m\({}^{2}\) & Piezoelectric stress constants at X-axis \\ \(\mathrm{e}_{33}\) & 23.24 & C/m\({}^{2}\) & Piezoelectric stress constants at Y-axis \\ \(\mathrm{e}_{15}^{\mathrm{E}}\) & \(-\)6.62 & C/m\({}^{2}\) & Piezoelectric stress constants at Z-axis \\ \(\mathrm{e}_{33}^{\mathrm{E}}\) & 1433.6 & / & Relative dielectric constant \\ \(\varepsilon_{r11}^{\mathrm{E}}\) & 1704.4 & / & Stress-charge constant \\ \(\rho\) & 7500 & kg/m\({}^{3}\) & Density \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material parameters of PZT-5H.  
Figure 4: Spherical harvester energy.  
After assigning each part to corresponding materials, a base vector coordinate system was defined so that the piezoelectric material was polarized along the direction of the load. A uniform load of 0.3 MPa was set at the top of the concrete column with the direction perpendicular to its upper surface, and a uniform circumferential pressure of 0.2 MPa was set. At the same time, fixed constraints were set at the bottom of concrete columns. The model set the ground boundary as the bottom of the piezoelectric layer, the terminal boundary as the top of the piezoelectric layer, and the terminal type as electric charge. The initial potential of the piezoelectric layer was 0, and the zero-charge boundary was set in the circumferential direction.