Open AccessFREE VIBRATION OF TAPERED FUNCTIONALLY GRADED CARBON NANOTUBE-REINFORCED COMPOSITE BEAMS USING A HIERARCHICAL BEAM ELEMENT
Author(s) -
Trinh Thi Hien
Publication year - 2020
Publication title -
vietnam journal of science and technology/science and technology
Language(s) - English
Resource type - Journals
eISSN - 2815-5874
pISSN - 2525-2518
DOI - 10.15625/2525-2518/57/6a/14643
Subject(s) - materials science , carbon nanotube , vibration , beam (structure) , composite material , volume fraction , finite element method , timoshenko beam theory , composite number , boundary value problem , aspect ratio (aeronautics) , displacement field , displacement (psychology) , structural engineering , mathematics , physics , mathematical analysis , acoustics , engineering , psychology , psychotherapist
Free vibration of tapered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams is investigated. The beams with four types of carbon nanotube distribution in the thickness, namely the uniform (UD-CNT), X-type (FGX-CNT), A-type (FGA-CNT) and O-type (FGO-CNT), are assumed to be linearly tapered in longitudinal direction by three different taper cases. Based on the first-order shear deformation theory, equations of motion with variable coefficients are derived from Hamilton’s principle. Using hierarchical functions to interpolate the displacement field, a two-node beam element with nine degrees of freedom is formulated and employed to compute frequencies of the beams. The accuracy of the derived formulation is confirmed by comparing frequencies obtained in the present work with the published data. The effects of the total CNT volume fraction, CNT distribution type, taper cases, taper ratio, aspect ratio, boundary conditions, etc., on the vibration characteristics of the beams are examined and discussed.