On Axial Constant Acceleration Movement and Small Transverse Vibrations of Membrane Panel

Abstract

An axially movement of the elastic web with small transverse vibrations is considered. It is supposed that the web movement described by the model of continuous elastic membrane panel is with a constant acceleration and is under action of centripetal, Coriolis, transverse inertial and in-plane tension forces. There are presented the transformations reduced the considered defining differential equation to Gauss hypergeometric equation. The total solution of this equation is presented by the help of hypergeometric series, the analysis of panel movement with a constant acceleration and arising vibrations is performed.