Free Linear Vibration of Self-Pressurized Foil Bearings

A foil bearing is formed when a flexible medium travels across a stationary rigid surface and entrains a thin layer of fluid that lubricates the relative sliding motion. Such bearings are used in magnetic tape drives to prevent excessive wear of the recording head and tape interface. In the one dimensional model considered here, the tape is approximated as an axially moving Euler Bernoulli beam under tension, and the air pressure in the bearing region satisfies Reynolds equation for unsteady compressible flow