## 1 Introduction
Figure 1: Schematic views of a one-pad journal gas foil bearing (GFB) with top and bump foil structures and gas foil-polymer bearing (GFPB) with top and bump foil structures as well as a polymer layer. These simple elastic foundation models [7; 8; 9] of bump foils neglect the elasticity of the top foil and consider them as an elastic foundation having a uniform stiffness coefficient. The consideration of all the effects on the properties of bearing structures is limited. This is because the stiffness coefficient is determined only by the geometry and material of the bump foil and/or dry-friction coefficients and not operation conditions. However, in practice, structural properties of the sub-structures significantly vary with the rotor speeds, deformations of the sub-structures, operation temperatures, and static and dynamic loads [3; 11; 12]. Recently, inducing a change in the mechanical properties of the sub-structures by introducing some high damping materials in the top and bump foil structures to stabilize the rotor-bearing system is receiving increased attention. [PERSON] et al. [13; 14] introduced viscoelastic materials into GFBs to increase the damping characteristics of the sub-structures. These viscoelastic GFBs comprised a series of laminated structures, i.e., viscoelastic material-based top and bump foils. The experiments showed that the enhanced structural damping lowered the amplitudes of the synchronous motion near the critical speed of the rotor-bearing system. [PERSON] et al. [3] experimentally evaluated the effects of high-damping sub-structures on the rotordynamic performance. The test bearings were one-pad GFBs and GFPBs with high-damping bump foil and polymer sub-structures. By conducting the 1-DOF dynamic loading tests of a flat specimen of the bearing sub-structure, they found out that the GFPBs had lower structural stiffness coefficients and higher structural loss factors than the GFBs. The rotordynamic performance measurements revealed that the GFPBs delayed the occurrence of the sub-synchronous motions and lowered the peak amplitude of the synchronous motions near the critical speed. [PERSON] et al. [15; 16; 17] performed a protective coating of the top foil with a thin fluoropolymer layer to reduce bearing friction and wear in GFBs. The rotordynamic experiment of bearings were carried out at high speeds and elevated temperatures from 20 to 290\({}^{\circ}\), which are in conditions that are typical for micro-turbine operation. Furthermore, authors examined static characteristics of the bearings via static-load deflection tests. Their work suggests that the polymer layer is sufficiently applicable to GFBs in turbomachinery running in relatively high-speed and high-temperature environments. In addition, polymers have been applied to various components of rotating machinery such as a compressor impeller, a nozzle body, a ball bearing cage, and a bushing [18; 19; 20; 21]. Similar to the earlier studies [3; 13; 14], introducing high-damping materials in the sub-structures of the GFBs was a useful solution for improving the rotordynamic stability. However, the authors in the studies did not investigate the underlying reason for this effectiveness in improving the rotordynamic stability. Without understanding the background mechanism of GFPBs, it is difficult to expect their widespread usage even if they provide outstanding rotordynamic performance. Absence of a reliable prediction model for the structures of GFPBs also impedes the widespread usage of the bearings. This study aims to develop a simple model for structural elasticity of GFPBs and examine stability performance of GFPBs using the model. The following work includes the structural model development of GFPBs based on [PERSON]'s law for the cylinder-shaped polymer layer, and the model is validated via the static-load deflection tests with a fabricated test GFPB with nitrile butadiene rubber. Static load versus displacement curve is used to validate the simple structural model.