## 6 Results and Discussion
### Static Analysis  
The static performance of the C-GFBs is compared with that of the shimmed GFBs to investigate the effects of structural compliance of the PZT actuators on the bearing performance. It is assumed that three metal shims, that are inserted between the foil structures and bearing housing, have an identical configuration to the C-GFB: the angular width of 27.7\({}^{\circ}\) and locations of 60\({}^{\circ}\), 180\({}^{\circ}\), and 300\({}^{\circ}\), whereas the thicknesses are set to the base piezoelectric deformations of the PZT actuators, given in Figure 8. Note that the mechanical preloads of shimmed GFBs do not undergo reductions in structural stiffness in the shim regions, unlike the piezoelectric preloads of C-GFBs, due to the metal shim's rigidity. Figure 9 illustrates the predicted mid-plane gas film pressure and thickness distributions of (a) C-GFB and (b) shimmed GFB under a rotational speed of 50 krpm. Both the C-GFB and shimmed GFB exhibit typical pressure and film thickness distributions of circular GFB without preload at the driving voltage of 0 V and shim thickness of 0. Figure 8: Comparison of C-GFB to shimmed GFB with identical mechanical preloads. Meanwhile, three pressure peaks are generated due to the preload effects, i.e., gas-film wedge effects, of significant thickness reductions in the gas film around three preload regions for both the C-GFB and shimmed GFB, increasing with the strength of the preload. However, the C-GFB exhibits smaller pressure peaks and higher minimum film thickness than the shimmed GFB. The difference is particularly evident at the PZT actuator #2 (180\({}^{\circ}\)) at the loaded region. This observation implies that the mechanical compression of the piezoelectric preloads occurs to a significant level owing to the gas-film pressure due to the PZT stack compliance. As a result, the PZT actuators enhance the gas-film pressure in the upper stinger regions. However, this is accompanied by the mechanical deflection caused by the gas-film pressure, which results in the generation of pressure peaks smaller than those on the shimmed GFB. Figure 10 illustrates the predicted local gas-film pressure versus rotational speeds at the mechanical preload locations for the C-GFB and shimmed GFB. The rotational speed ranges from 10 to 90 krpm. As expected, all the pressures of both GFBs tend to increase with higher driving voltages and shim thicknesses as well as higher rotational speeds. The pressures at the loaded location (\(\theta\) = 180\({}^{\circ}\)) exhibit the highest level due to the minimized film thickness. The C-GFB exhibits lower pressure distribution than the shimmed GFB with smaller piezoelectric preloads due to the compression of PZT actuators. In particular, the pressures at \(\theta\) = 180\({}^{\circ}\) tend to firstly decrease then increase from the rotating speed of 10 to 90 krpm, due to the combined effects of the rotational speed and journal center position. The higher rotational speed generates a higher-pressure distribution because the flow rate of the air in the bearing clearance also increases. In addition, the journal generally increases due to the higher-pressure distribution, and its equilibrium position moves toward the bearing center, while also increasing the gas film thickness around \(\theta\) = 180\({}^{\circ}\) so that the pressure at the location reduces. This tendency is higher in the shimmed GFB. Figure 9: Predicted mid-plane gas film pressure and thickness distributions of (**a**) C-GFB and (**b**) shimmed GFB under a rotational speed of 50 krpm. Figure 11 illustrates the predicted piezoelectric preloads versus rotational speeds at the preload locations for the C-GFB. Note that the peak gas-film pressures at the preload locations push the PZT actuators upwards, as well as the foil structure. Therefore, the compliant piezoelectric preloads show opposite trends to the gas-film pressures as the rotational speed increases.