Vibration analysis of pre-twisted rotating beams

Abstract

A new linearly pretwisted rotating Timoshenko beam element, which has two nodes and four degrees of freedom per node, is developed and subsequently used for vibration analysis of pretwisted beams with uniform rectangular cross-section. First, displacement functions based on two coupled displacement fields (the polynomial coefficients are coupled through consideration of the differential equations of equilibrium) are derived for pretwisted beams. Next, the stiffness and mass matrices of the finite element model are obtained by using the energy expressions. Finally, the natural frequencies of pretwisted rotating Timoshenko beams are obtained and compared with previously published both theoretical and experimental results to confirm the accuracy and efficiency of the present model. The new pretwisted Timoshenko beam element has good convergence characteristics and excellent agreement is found with the previous studies.