Free vibration analysis of a non-uniform axially functionally graded cantilever beam with a tip body

Abstract

© 2017, Springer-Verlag Berlin Heidelberg. This paper considers the free vibrations of the non-uniform axially functionally graded cantilever beam with a tip body. It is assumed that the mass center of the tip body is eccentrically displaced in both axial and transverse direction relative to the beam tip. All considerations are carried out within the Euler–Bernoulli beam theory. The in-plane transverse and axial deformations of the beam are considered. It is shown that there is a coupling between the axial and transverse deformations of the cantilever beam due to the tip body mass center eccentricity in the transverse direction. An universal, numerically efficient rigid element method which is able to analyze the cantilever beam with any law of changes of the geometric parameters of the cross section or the characteristics of the material along the beam was formed. Theoretical considerations are accompanied by numerical examples. There is a good agreement of the results obtained with the results available in the literature.