Hierarchical finite element method for rotating beams

The free vibration characteristics of rotating beams are analyzed by means of a finite element method of hierarchical form, in which the displacement function for the element is taken to be a polynomial of variable degree. The first four terms of the polynomial are expressed in terms of the displacements and slopes at the extremities of the elements, and the rest of the terms are considered as internal degrees of freedom. Numerical results are presented for cantilever beams with uniform, non-uniform and discontinuous sectional properties. A comparison of the present results with those in the published literature indicates that the present relatively simple formulation is as efficient as the other well established techniques. Finally, some clarification is also provided of certain subtle issues concerning the accuracy of the finite element solution and monotonic convergence characteristics, and their dependence on the arithmetic precision of the computer employed is indicated.