An Efficient Approach for Free Vibration Behaviour of Non-Uniform and Non-Homogeneous Helices

The paper presents an efficient numerical method for free vibration analysis of non-uniform and non-homogeneous cylindrical helices. Power law distribution is used for the variation of the material properties along the axial direction of rods. The derivation of the governing equations are carried out by the Timoshenko’s beam theory. Obtained ordinary differential equations of the problems are solved using the complementary functions and stiffness matrix methods. Numerical examples are given to highlight the effects of varying geometric and material properties on free vibration. Proposed method requires a small number of elements in order to yield agreeable results. The computed results are compared with those reported in the literature and obtained from the finite element ANSYS software.