Free vibration analysis of functionally graded cylindrical helices with variable cross-section

The main purpose of this study is to investigate free vibrations of cylindrical helical rods with variable cross-section, composed of functionally graded materials, which may be used to model environmental effects. The material variation is considered to be along the rod axis. Governing differential equations of the free vibration are obtained via Timoshenko's beam theory, where axial and shear deformations and rotary inertia are taken into consideration. The governing equations are solved numerically by using the transfer matrix method. The effects of cross-section variation (beta(sec)), material gradient index (beta(mat)), helix pitch angle (alpha), and number of active coils (n) on the frequencies are investigated. All results are compared with the ANSYS solutions, in which a very well approximation is achieved. (C) 2020 Elsevier Ltd. All rights reserved.