Dynamic simulation of the Wilberforce pendulum using constrained spatial nonlinear beam finite elements

More than 100 years ago, Lionel Robert Wilberforce did investigations On the Vibrations of a Loaded Spiral Spring [1]. The spring was clamped at its upper side and on the other side, perpendicular to the spring axis, a steel cylinder was attached. Four screws with adjustable nuts were symmetrically attached around the cylinder in order to change its moment of inertia (Fig. 1). In this paper the Wilberforce pendulum is modeled by a rigid body attached to a constrained spatial nonlinear Timoshenko beam, discretized with B-spline shape functions. As shown by a numerical experiment, the presented model is capable of reproducing the characteristic pendulum motion.