Finite Element Analysis Of An Axially Moving Beam, Part I: Time Integration

Abstract Axially moving materials arise in problems associated with spacecraft antennas, pipes conveying fluid and telescopic robotic manipulators. Axially moving beams are a special class of axially moving materials, in which the axially moving material is modelled as a slender beam and the mechanism of elastic deformation is transverse bending. The mass of this system is not constant and the general analytical solution to the equation of motion is not known. In this study, numerical solutions are obtained using finite element analysis. However, instead of following the obvious (but cumbersome) approach of using fixed-size elements and increasing their number, in a step-wise fashion, as mass elements enter the domain of interest, a more elegant approach is followed wherein the number of elements is fixed, while the sizes of the elements change with time. To this end, a variable-domain beam finite element the size of which is a prescribed function of time is formulated in Part I. The accuracy of this variable-domain beam element is demonstrated through the time-integration of equations of motion using various extrusion profiles. The effects of wall flexibility, tip mass, and high frequency axial motion perturbations to the transverse response of the flexible extendible beam are also examined.