Natural frequency of axially functionally graded, tapered cantilever beams with tip masses

• Published in: Engineering structures Vol. 187; pp. 34 - 42
• Main Author: Mahmoud, M.A.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 15.05.2019; Elsevier BV
• Subjects: Axially functionally graded; Beam theory (structures); Cantilever beams; Cantilevers; Euler-Bernoulli beams; Free vibration; Functionally gradient materials; Myklestad Method; Resonant frequencies; Tapered cantilever; Tip mass; Axially functionally graded; Tapered cantilever; Myklestad Method; Tip mass; Free vibration
• ISSN: 0141-0296; 1873-7323
• DOI: 10.1016/j.engstruct.2019.02.043

•A general numerical solution for vibration analysis of AFG beams is presented.•The accuracy of the method is verified by comparison with many published results.•The method is verified for non-uniform beams of different material grading functions.•Solutions presented for mass-loaded AFG cantilevers, a scarce case in the literature. This article presents a general solution for the free transverse vibration of non-uniform, axially functionally graded cantilevers loaded at the tips with point masses. Attention is focused on undamped cantilevers that fall within the range of validity of Euler-Bernoulli beam theory. The Myklestad Method is shown to be an efficient and accurate tool for this purpose. Results are presented for a number of cases of different beam geometries and material gradients.