Numerical computation of a damped slewing beam with tip mass

This paper describes an analytical model for a beam system, based on a modified Timoshenko theory, where the beam is pinned to a hub driven by an actuator at one end and is subject to a heavy load at the other end. A new efficient computational algorithm is then proposed for solving the higher-order non-canonical partial differential equation model, which is developed based on the generalized difference method. This allows a suitable selection of different trial and test spaces, so as to improve the computational efficiency while preserving the high convergence rate of the standard finite element method. With the trial space of cubic Hermite finite elements and the test space of piecewise linear functions, the computational scheme reduces to a semi-discretized or even fully discretized computational algorithm. A numerical simulation result is included to visualize the theoretical modelling and computational results.