The influence of bending and shear stiffness and rotational inertia in vibrations of cables: An analytical approach

The main objective of this work is to analyze the influence of bending and shear stiffness, and rotational inertia in the natural frequencies of overhead transmission line conductors, and to compare the results with a vibrating string, where only geometrical stiffness is considered. Five formulations, based on Bernoulli’s and Timoshenko’s beam theories, taking into account the effects of geometrical, bending and shear stiffness and rotational inertia are considered here. They are also based on the assumption that the cable is inextensible. The equation of motion of the vibrating cable is developed analytically, assuming small strains. The Newton–Raphson method is employed for the solution of the nonlinear equations. A numerical example is presented and the results are compared with solutions obtained from the technical literature.