Quasi-static and dynamic response of viscoelastic helical rods

In this study, the dynamic behaviour of cylindrical helical rods made of linear viscoelastic materials are investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial rods obtained using the Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, effect of rotary inertia, and shear and axial deformations are considered in the formulation. The material of the rod is assumed to be homogeneous, isotropic and linear viscoelastic. In the viscoelastic material case, according to the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace domain. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem. In the solutions, the Kelvin model is employed. The solutions obtained are transformed to the real space using the Durbinʹs numerical inverse Laplace transform method. Numerical results for quasi-static and dynamic response of viscoelastic models are presented in the form of graphics.