Dynamic analysis of cylindrical and non-cylindrical viscoelastic helical rods with functionally graded material and variable cross-section

In this thesis, dynamic behaviour of cylindrical and non-cylindrical viscoelastic helical rods with functionally graded material and variable cross-section was investigated. The differential equations governing the dynamic behaviour of the helical rods were derived by the Timoshenko beam theory. Axial and shear deformations were taken into consideration in the obtained differential equations. Ordinary differential equations were then solved in the Laplace domain by the transfer matrix method. For the viscoelastic solutions, elastic constants were replaced with their viscoelastic counterparts in Laplace domain by using the correspondence principle. Kelvin viscoelastic model was used for the solutions. Obtained results were transferred from Laplace domain to the time domain by the Modified Durbin's numerical inverse Laplace transform algorithm. The effects of section variation, material variation, active number of turns, helix pitch angle, helix radius ratio and damping ratio on the dynamic behaviour of cylindrical and non-cylindrical helical rods were investigated. It can be seen that obtained results with proposed model are in good agreement with the ones available in the literature and the ones acquired from finite element based program ANSYS.