Forced Vibration of Cylindrical Helical Rods Subjected to Impulsive Loads

Abstract

In this study, the forced vibration of cylindrical helical rods subjected to impulsive loads is theoretically investigated in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The governing equations for naturally twisted and curved space rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The material of the rod is assumed to be homogeneous, linear elastic, and isotropic. The axial and shear deformations are also taken into account in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The desired accuracy is obtained by taking only a few elements. The solutions obtained are transformed to the real space using the Durbin’s numerical inverse Laplace transform method. The free and forced vibrations of cylindrical helical rods are analyzed through various example. The results obtained in this study are found to be in a good agreement with those available in the literature.