ON AXIAL MOTION OF THE PANEL UNDER MECHANICAL AND TEMPERATURE ACTION

Abstract

The problems of the stability of axially moving materials and the elastic web behavior sensitivity with respect to an external loading are investigated on the basis of the classic mathematical physics and mechanics methods. It is considered the process of rectilinear motion of a simply supported elastic web modelled as a panel which moves with a constant velocity and is on the external thermomechanical actions. Small transverse elastic displacements of the panel are described by a fourth-order differential equation that includes the terms expressing the action of in-plane tension and out-of-plane centrifugal forces and the terms taking into account a thermomechanical action. Two important cases are investigated separately: the divergence of the panel loaded by in-plane thermomechanical tension and the deformation of the beam subjected to combined thermomechanical bending and tension. In both cases the considered problems have been studied analytically and the solutions have been found in an explicit form.

Keywords: mathematical modelling, axially moving panel, divergence, thermomechanical instability.