The fluid-structure interaction in supporting a thin flexible cylindrical web with an air cushion

摘要

The mechanics of the fluid-structure interaction between a thin flexible web, wrapped around a cylindrical drum (reverser), and the air cushion formed by external pressurization through the holes of this drum is analyzed. Derivation of a "new" theory for the moderately large deflections of a thin cylindrical shell to model the web is presented. This theory allows for large web deflections, while using a self-adjusting strain-free reference state for the web in order to keep the circumferential web tension around a constant level. The theory also incorporates the redistribution of the in-plane stress resultants in the axial and shear directions using the Airy stress function. The air-flow is averaged over the height direction of the web-reverser clearance. The surface area of the pressure holes is averaged locally over the total reverser surface. The resulting equations are a modified form of the Navier-Stokes and mass balance equations with nonlinear source terms. The coupled fluid-structure system is solved numerically. The mechanics of the interaction between the web deflections and the air cushion generated by the reverser is explained. The effects of the problem parameters on the overall equilibrium are presented. Parameter distributions which cause the web to contact the reverser are identified, and suggestions are made to avoid this state.