Dynamics Of Axially Moving Beams Made Of Functionally Graded Materials

Abstract

Problems related to the vibrations of axially moving flexible beams made of functionally
graded materials are addressed. The problem of an axially moving beam may be interpreted as a telescopic
system where the mass is not constant, the mechanism of elastic deformation is transverse bending.
A thin-walled beam with annular cross-section is analyzed, where a continuously graded variation
in the composition of ceramic and metal phases across the wall thickness with a simple power law is
considered.
In this paper a finite element scheme is employed to obtain numerical approximations to the variational
equation of the problem. Normally, finite element approaches use fixed-size elements, however
for this kind of problems the increase of the number of elements, step by step as the mass enters is a
cumbersome task. For this reason an approach based on a beam-element of variable domain is adopted.
The length of the element is a prescribed function of the time.
Results highlighting the effects of the beam flexibility, tip mass and material constituents on the
dynamics of the axially moving beams are presented and the corresponding conclusions are given.