Purpose This paper aims to propose novel flexible structure-supported tilting-pad aerostatic bearings and to improve operational stability and vibration reduction of aerostatic bearings. Design/methodology/approach The authors established an aerostatic bearing-rotor test rig and designed two aerostatic tilting-pad bearings with different flexible support structure and an ordinary aerostatic tilting-pad bearing and then examined their effects in dynamic performance to assess the vibration reduction performance of different flexible structures. Furthermore, the authors proposed three gas supply methods and conducted experiments to study the influence of gas supply methods in the performance of bearings. Findings The experimental results show that among the three structures, the double-layer flexible structure-supported tilting-pad bearing demonstrates outstanding vibration damping performance and it significantly enhances the operational stability of the bearing-rotor system. Furthermore, the experimental results indicate that the gas supply method has a significant impact on the performance of the aerostatic bearing. There is a certain pressure difference between the gas supply pressure for the loading pads and that for the nonloading pads, which is advantageous for increasing the operational stability and reducing system vibration. Originality/value The authors designed novel flexible aerostatic tilting-pad journal bearing structures, which can enhance the operational stability and reduce vibrations of the bearing. Additionally, this article proposes an air supply method advantageous for increasing the stability of the bearing and reducing system vibrations.