Transient response of functionally graded non-uniform cylindrical helical rods

This paper have the objective of investigating forced vibration behaviour of axially functionally graded cylindrical helices with variable cross-section. An algorithm is developed in order to solve corresponding problems. The ordinary differential equations governing the dynamic behaviour of cylindrical helices are determined in Laplace domain by using Timoshenko beam theory. Then transfer matrix method is implemented for the solution, including shear and axial deformation effects. Obtained results are transferred to time domain using Durbin's modified numerical inverse algorithm for Laplace transform. A benchmark problem has been solved to check the accuracy of developed algorithm then a parametric study is conducted considering the effects of material gradient index (beta(mat)), section variation (beta(sec)) and number of active turns (n). Results are compared with solutions attained from ANSYS for verification.