A dynamic model of a rotating shaft on two textured hydrodynamic journal bearings is presented. The hydrodynamic mean pressure is computed using multi-scale periodic homogenization and is projected on a flexible shaft with internal damping. Harmonic Balance Method (HBM) is used to study the limit cycles of unbalance response of the coupled system discretized by Finite Element Method (FEM). Stability is analyzed with Floquet multipliers computation. An example of an isotropic texturing pattern representing Laser dimples on a lightweight rotor is analyzed. Vibration amplitude and stability zone are compared with plain bearing lubrication. It is shown in an example that full surface texturing leads to relatively higher vibration amplitude compared to plain bearings.